prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: Where was Margaret Way born and where did she die?

Read the following text and answer briefly.

Context 1: Margaret Way (b  Brisbane d  Cleveland, Queensland, Australia ) was an Australian writer of romance novels and women's fiction  A prolific author, Way wrote more than 120 novels since 1970, many through Mills & Boon, a romance imprint of British publisher Harlequin UK Ltd , owned by Harlequin Enterprises 

Biography
Before her marriage, she was a well-known pianist, teacher, vocal coach and accompanist  She began writing when her son, Laurence Way, was born, a friend took a pile of Mills & Boon books to her, she read all and decided that she also could write these types of novels  She began to write and promote her country with her stories set in Australia  She sold her first novels in 1970  Margaret Way lives with her family in her native Brisbane  Beginning in 2013, Margaret began to self-publish, releasing her first "e-book" mid-July 

Margaret died on the 10th of August 2022 in Cleveland, Queensland 

Bibliography

Single Novels
King Country (1970)
Blaze of Silk (1970)
The Time of the Jacaranda (1970)
Bauhinia Junction (1971)
Man from Bahl Bahla (1971)
Summer Magic (1971)
Return to Belle Amber (1971)
Ring of Jade (1972)
Copper Moon (1972)
Rainbow Bird (1972)
Man Like Daintree (1972)
Noonfire (1972)
Storm Over Mandargi (1973)
Wind River (1973)
Love Theme (1974)
McCabe's Kingdom (1974)
Sweet Sundown (1974)
Reeds of Honey (1975)
Storm Flower (1975)
Lesson in Loving (1975)
Flight into Yesterday (1976)
Red Cliffs of Malpara (1976)
Man on Half-moon (1976)
Swan's Reach (1976)
Mutiny in Paradise (1977)
One Way Ticket (1977)
Portrait of Jaime (1977)
Black Ingo (1977)
Awakening Flame (1978)
Wild Swan (1978)
Ring of Fire (1978)
Wake the Sleeping Tiger (1978)
Valley of the Moon (1979)
White Magnolia (1979)
Winds of Heaven (1979)
Blue Lotus (1979)
Butterfly and the Baron (1979)
Golden Puma (1980)
Temple of Fire (1980)
Lord of the High Valley (1980)
Flamingo Park (1980)
North of Capricorn (1981)
Season for Change (1981)
Shadow Dance (1981)
McIvor Affair (1981)
Home to Morning Star (1981)
Broken Rhapsody (1982)
The Silver Veil (1982)
Spellbound (1982)
Hunter's Moon (1982)
Girl at Cobalt Creek (1983)
No Alternative (1983)
House of Memories (1983)
Almost a Stranger (1984)
A place called Rambulara (1984)
Fallen Idol (1984)
Hunt the Sun (1985)
Eagle's Ridge (1985)
The Tiger's Cage (1986)
Innocent in Eden (1986)
Diamond Valley (1986)
Morning Glory (1988)
Devil Moon (1988)
Mowana Magic (1988)
Hungry Heart (1988)
Rise of an Eagle (1988)
One Fateful Summer (1993)
The Carradine Brand (1994)
Holding on to Alex (1997)
The Australian Heiress (1997)
Claiming His Child (1999)
The Cattleman's Bride (2000)
The Cattle Baron (2001)
The Husbands of the Outback (2001)
Secrets of the Outback (2002)
With This Ring (2003)
Innocent Mistress (2004)
Cattle Rancher, Convenient Wife (2007)
Outback Marriages (2007)
Promoted: Nanny to Wife (2007)
Cattle Rancher, Secret Son (2007)
Genni's Dilemma (2008)
Bride At Briar Ridge (2009)
Outback Heiress, Surprise Proposal (2009)
Cattle Baron, Nanny Needed (2009)

Legends of the Outback Series
Mail Order Marriage (1999)
The Bridesmaid's Wedding (2000)
The English Bride (2000)
A Wife at Kimbara (2000)

Koomera Crossing Series
Sarah's Baby (2003)
Runaway Wife (2003)
Outback Bridegroom (2003)
Outback Surrender (2003)
Home to Eden (2004)

McIvor Sisters Series
The Outback Engagement (2005)
Marriage at Murraree (2005)

Men Of The Outback Series
The Cattleman (2006)
The Cattle Baron's Bride (2006)
Her Outback Protector (2006)
The Horseman (2006)

Outback Marriages Series
Outback Man Seeks Wife (2007)
Cattle Rancher, Convenient Wife (2007)

Barons of the Outback Series Multi-Author
Wedding At Wangaree Valley (2008)
Bride At Briar's Ridge (2008)

Family Ties Multi-Author
Once Burned (1995)

Hitched! Multi-Author
A Faulkner Possession (1996)

Simply the Best Multi-Author
Georgia and the Tycoon (1997)

The Big Event Multi-Author
Beresford's Bride (1998)

Guardian Angels Multi-Author
Gabriel's Mission (1998)

Australians Series Multi-Author
7  Her Outback Man (1998)
17  Master of Maramba (2001)
19  Outback Fire (2001)
22  Mistaken Mistress (2002)
24  Outback Angel (2002)
33  The Australian Tycoon's Proposal (2004)
35  His Heiress Wife (2004)

Marrying the Boss Series Multi-Author
Boardroom Proposal (1999)

Contract Brides Series Multi-Author
Strategy for Marriage (2002)

Everlasting Love Series Multi-Author
Hidden Legacy (2008)

Diamond Brides Series Multi-Author
The Australian's Society Bride (2008)

Collections
Summer Magic / Ring of Jade / Noonfire (1981)
Wife at Kimbara / Bridesmaid's Wedding (2005)

Omnibus in Collaboration
Pretty Witch / Without Any Amazement / Storm Over Mandargi (1977) (with Lucy Gillen and Margaret Malcolm)
Dear Caliban / Heart of the Eagle / Swans' Reach (1978) (with Jane Donnelly and Elizabeth Graham)
The Bonds of Matrimony / Dragon Island / Reeds of Honey (1979) (with Elizabeth Hunter and Henrietta Reid)
The Man Outside / Castles in Spain / McCabe's Kingdom (1979) (with Jane Donnelly and Rebecca Stratton)
Winds From The Sea / Island of Darkness / Wind River (1979) (with Margaret Pargeter and Rebecca Stratton)
Moorland Magic / Tree of Idleness / Sweet Sundown (1980) (with Elizabeth Ashton and Elizabeth Hunter)
The Shifting Sands / Portrait of Jaime / Touched by Fire (1982) (with Jane Donnelly and Kay Thorpe)
Head of Chancery / Wild Heart / One-Way Ticket (1986) (with Betty Beaty and Doris Smith)
Heart of the Scorpion / The Winds of Heaven / Sweet Compulsion (1987) (with Janice Gray and Victoria Woolf)
One Brief Sweet Hour / Once More With Feeling / Blue Lotus (1990) (with Jane Arbor and Natalie Sparks)
Marry Me Cowboy (1995) (with Janet Dailey, Susan Fox and Anne McAllister)
Husbands on Horseback (1996) (with Diana Palmer)
Wedlocked (1999) (with Day Leclaire and Anne McAllister)
Mistletoe Magic (1999) (with Betty Neels and Rebecca Winters)
The Australians (2000) (with Helen Bianchin and Miranda Lee)
Weddings Down Under (2001) (with Helen Bianchin and Jessica Hart)
Outback Husbands (2002) (with Marion Lennox)
The Mother's Day Collection (2002) (with Helen Dickson and Kate Hoffmann)
Australian Nights (2003) (with Miranda Lee)
Outback Weddings (2003) (with Barbara Hannay)
Australian Playboys (2003) (with Helen Bianchin and Marion Lennox)
Australian Tycoons (2004) (with Emma Darcy and Marion Lennox)
A Mother's Day Gift (2004) (with Anne Ashley and Lucy Monroe)
White Wedding (2004) (with Judy Christenberry and Jessica Steele)
A Christmas Engagement (2004) (with Sara Craven and Jessica Matthews)
A Very Special Mother's Day (2005) (with Anne Herries)
All I Want for Christmas    (2005) (with Betty Neels and Jessica Steele)
The Mills and Boon Collection (2006) (with Caroline Anderson and Penny Jordan)
Outback Desire (2006) (with Emma Darcy and Carol Marinelli)
To Mum, with Love (2006) (with Rebecca Winters)
Australian Heroes (2007) (with Marion Lennox and Fiona McArthur)
Tall, Dark and Sexy (2008) (with Caroline Anderson and Helen Bianchin)
The Boss's Proposal (2008) (with Jessica Steele and Patricia Thayer)
Island Heat / Outback Man Seeks Wife / Prince's Forbidden Virgin / One Night Before Marriage / Their Lost-and-found Family / Single Dad's Marriage Wish (2008) (with Robyn Donald, Marion Lennox, Carol Marinelli, Sarah Mayberry and Anne Oliver)
Australian Billionaires (2009) (with Jennie Adams and Amy Andrews)
Cattle Baron : Nanny Needed / Bachelor Dad on Her Doorstep (2009) (with Michelle Douglas)

External links
Margaret Way at Harlequin Enterprises Ltd

Australian romantic fiction writers
Australian women novelists
Living people
Year of birth missing (living people)
Women romantic fiction writers
Context 2: The future of mobile CPUs, part 1: Today’s fork in the road | Ars Technica
2013 may be a big year for the evolution of smartphones and tablets 
Mobile computing's rise from niche market to the mainstream is among the most significant technological trends in our lifetimes  And to a large extent, it's been driven by the bounty of Moore’s Law—the rule that transistor density doubles every 24 months  Initially, most mobile devices relied on highly specialized hardware to meet stringent power and size budgets  But with so many transistors available, devices inevitably grew general-purpose capabilities  Most likely, that wasn't even the real motivation  The initial desire was probably to reduce costs by creating a more flexible software ecosystem with better re-use and faster time to market  As such, the first smartphones were very much a novelty, and it took many years before the world realized the potential of such devices  Apple played a major role by creating innovative smartphones that consumers craved and quickly adopted 
To some extent, this is where we still stand today  Smartphones are still (relatively) expensive and primarily interesting to the developed world  But over the next 10 years, this too will change  As Moore’s Law rolls on, the cost of a low-end smartphone will decline  At some point, the incremental cost will be quite minimal and many feature phones of today will be supplanted by smartphones  A $650 unsubsidized phone is well beyond the reach of most of the world compared to a $20 feature phone, but a $30 to $40 smartphone would naturally be very popular 
In this grand progression, 2013 will certainly be a significant milestone for mobile devices, smartphones and beyond  It's likely to be the first year in which tablets out-ship notebooks in the US  And in the coming years, this will lead to a confluence of high-end tablets and ultra-mobile notebooks as the world figures out how these devices co-exist, blend, hybridize, and/or merge 
Against this backdrop, in this two-part series, we'll explore the major trends and evolution for mobile SoCs  More importantly, we'll look to where the major vendors are likely going in the next several years 
Tablet and phone divergence
While phones and tablets are mobile devices that often share a great deal of software, it's becoming increasingly clear the two are very different products  These two markets have started to diverge and will continue doing so over time 
From a technical perspective, smartphones are far more compact and power constrained  Smartphone SoCs are limited to around 1W, both by batteries and by thermal dissipation  The raison d’etre of a smartphone is connectivity, so a cellular modem is an absolute necessity  For the cost sensitive-models that make up the vast majority of the market, the modem is integrated into the SoC itself  High-end designs favor discrete modems with a greater power budget instead  The main smartphone OSes today are iOS and Android, though Windows is beginning to make an appearance (perhaps with Linux or BlackBerry on the horizon)  Just as importantly, phone vendors like HTC must pass government certification and win the approval of carriers  There is very much a walled-garden aspect, where carriers control which devices can be attached to their networks, and in some cases devices can only be sold through a certain carrier  The business model places consumers quite far removed from the actual hardware 
In contrast, tablets are far more akin to the PC both technically and economically  The power budget for tablet SoCs is much greater, up to 4W for a passively cooled device and as high as 7-8W for systems with fans  This alone means there is a much wider range of tablet designs than smartphones  Moreover, the default connectivity for tablets is Wi-Fi rather than a cellular modem  The vast majority of tablets do not have cellular modems, and even fewer customers actually purchase a wireless data plan  As a result, cellular modems are almost always optional discrete components of the platform  The software ecosystem is relatively similar, with Microsoft, Apple, and Google OSes available  Because tablets eschew cellular modems, the time to market is faster, and they are much more commonly sold directly to consumers rather than through carriers  In terms of usage models, tablets are much more PC-like, with reasonable-sized screens that make games and media more attractive 
Looking forward, these distinctions will likely become more pronounced  Many tablets today use high-end smartphone SoCs, but the difference in power targets and expected performance is quite large  As the markets grow in volume, SoCs will inevitably bifurcate to focus on one market or the other  Even today, Apple is doing so, with the A6 for phones and the larger A6X for tablets  Other vendors may need to wait a few years to have the requisite volume, but eventually the two markets will be clearly separate 
Horizontal business model evolution
Another aspect of the mobile device market that is currently in flux and likely to change in the coming years is the business model for the chip and system vendors  Currently, Apple is the only company truly pursuing a vertically integrated model, where all phones and tablets are based on Apple’s own SoC designs and iOS  The tight integration between hardware and software has been a huge boon for Apple, and it has yielded superb products 
Samsung is one of the few others companies that takes a vertically integrated approach to phones and tablets, although in truth its strategy seems to be ambivalent on that point  Unlike Apple, Samsung’s SoCs are readily available to third parties, and some Samsung devices, such as the S7562 Galaxy S Duos, use SoCs from competitors  More recently though, there has been a trend of Samsung devices using Samsung SoCs, at least for the premier products  For the moment, Samsung’s approach is best characterized as a hybrid, particularly as the company lacks a bespoke OS 
The rest of the major SoC vendors (e g , Intel, Qualcomm, Nvidia, TI, Mediatek, etc ) have stayed pretty far away from actual mobile devices  These companies tend to focus on horizontal business models that avoid competing with customers or suppliers 
In the long term, mobile devices are likely to evolve similarly to the PC and favor a horizontal business model  The real advantage is one of flexibility; as costs drop and the market expands, it will be increasingly necessary for vendors like HTC to offer a wide range of phones based on radically different SoCs  While a vertically integrated company like Apple can focus and maintain leadership in a specific (and highly lucrative) niche, it would be very difficult to expand in many growing areas of the market  The differences between an iPhone 6 and a $20 feature phone are tremendous and would be very difficult for a single company to bridge 
However, SoC vendors will attempt to reap the benefits of vertical integration by providing complete reference platforms to OEMs  Conceptually, this is a form of "optional" system integration, where the phone vendor or carrier can get the entire platform from the SoC supplier  This has the principal advantages of reducing time to market while also providing a baseline quality and experience for consumers  Currently, this approach has mostly been tested in emerging markets, but it's likely to become more common over time  There is a crucial distinction between reference platforms and vertical integration  Namely, OEMs can always choose to customize a platform to differentiate, and the SoC vendor avoids dealing with consumers directly  Typically, most of the customization is in terms of software on top of a base operating system 
Quote:Moreover, that will make the transition to a 10nm node even more difficult, as the foundries will have to move from 20nm interconnects to 10nm interconnects and skip a generation The advances in technology lately allowing components on such a small scale to even be envisioned, much less planned for, are truly amazing 
Off topic: show
I present the first generation 'non-technical' rock:
I don't think your horizontal market development theory is supported by facts  Samsung and Apple are more vertically oriented than their competition, for starters  I know this article is narrowly focused on the hardware, but MS and Intel getting into hardware, Amazon getting into hardware, Google buying Moto, this is all vertical integration  How can you support the idea that this trend will be reversed with no real justification? I'm sure mobile chips will continue to specialize, but I don't think this means what you think it means  Automobile companies started making their own engines and with rare exceptions, never went back to being more horizontal  Same with retail and their store brands  Same with cloud companies and their servers  Same with mobile companies and their OSs  The horizontal market of PCs created by long-lasting standards and loose hegemony is the exception, not the norm 
Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?
I'm not so sure about several things:1- Moore's law's relevance  Moore's Law is about ICs  ICs are not as big a part of mobile computers as they are of desktops, even of laptops: screens, batteries, radios are a huge part of tablets' and phones' costs, as opposed to the bare SoC + RAM 2- The tablet vs phone dichotomy  For some reason (probably price insensitivity due to subsidies), Phones have a tendency to be more powerful than Tablets, ie phone SoCs are more than good enough for tablets  Since the OS and peripherals are the same, it makes more sense to design and build just one type of SoC, and just disable the phone-modem part of it (even the other radios are still required: BT, Wifi, GPS   ), same as Intel disable cache and cores for their entry-level CPUs  Once you're fabbing a SoC, it makes more sense to make more of the same than to setup a separate run of a cut-down SoC on an older process, unless volumes are huge  We might still be getting previous-generation, well amortized SoCs in cheaper tablets, though 3- On the contrary, I see a tablet and phone convergence (the ugly phablet)  I'm patiently waiting for the new 6"+ phones to replace my Nook Color and Galaxy Note 1 with a single device 4- The advantage of diversity ? Software is becoming ever more important than hardware  Multiplying SoCs means multiplying product development costs, making support and updates more difficult    Again, unless volumes are huge, OEMs are probaly better off going the way of the car industry and using modular "platforms" housed in different chassis with various screen sizes, keyboards, radios, digitizers   I'm wondering why the "single device" trend does not figure in your analysis  Is it stillborn ? Does it have no impact nor dependency on/with SoCs ?
Samsung has its own bespoke OS: Bada and it is used on an extensive line of devices  I think there are numbers somewhere that it outsold Windows Phone 7 for a time 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?First mover advantage 
SoC? System on a Chip I guess?
You're way off on the Moore's Law/cost of smartphones point  The processors used in today's high-end smartphones are already cheap, around $25  And there are less expensive options if you want a lower end product  In fact, the hardware in the whole smartphone is relatively cheap  Analyst's estimate the Z10's materials cost around $160, the iPhone 5 around $140  They're using expensive glass and metals, then there's the battery, memory, etc  which means the processor is a small factor of the cost And then there's the jump from $140 in materials to the unsubsidized costs  The reason these phones cost $650 is because of the high margins these companies are able to get and the high cost of hardware design and/or software development  But the point is that making the processors 4 times better/cheaper isn't going to change the economics of the smartphone  What will change the economics is commoditized designs and software and cheaper materials all around  Then you'll have a $50 smartphone that's decent 
Last edited by ggeezz on Wed Feb 13, 2013 9:17 am
bigterp wrote:SoC? System on a Chip I guess?Yup 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries 
Quote:Currently, the only products using 3D integration are FPGAs from Xilinx,Doesn't Sony use it in the PS Vita? I thought I read somewhere that they had the CPU, main memory (2 dies) and video memory, so 4 dies in total, sitting on top of each other all on the same chip 
renoX wrote:gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries Exactly and I would clarify that it's all about margins, the difference between what it costs to make a chip and what it sells for  The margins for desktop and server processors is huge because a) the whole product is expensive so $200 to $1000 for the chip is acceptable, and b) Intel has huge advantages in that space and little competition So Intel can afford to do the R&D to stay ahead of the curve and keep their position  When your smartphone chip sells for $25 you can't do the R&D to leapfrog a company that sells Xeons for $1000 and Core i5's for $200 
I am happy to see Kanter here at Ars, I like his writing and he maintains Real World Tech, where Linus Torvalds often shows up to comment on CPU arch and other interesting topics 
ggeezz wrote:renoX wrote:gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Money and momentum, the x86 market is a huge money maker for Intel so it is able to recoup its huge investments for advanced foundries Exactly and I would clarify that it's all about margins, the difference between what it costs to make a chip and what it sells for  The margins for desktop and server processors is huge because a) the whole product is expensive so $200 to $1000 for the chip is acceptable, and b) Intel has huge advantages in that space and little competition So Intel can afford to do the R&D to stay ahead of the curve and keep their position  When your smartphone chip sells for $25 you can't do the R&D to leapfrog a company that sells Xeons for $1000 and Core i5's for $200 Spot on Intel are able to piggyback other development efforts off the highly lucrative mainstream x86 market which generates the huge sums of money to fund their amazing fab technology The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art 
solomonrex wrote:I don't think your horizontal market development theory is supported by facts  Samsung and Apple are more vertically oriented than their competition, for starters  I know this article is narrowly focused on the hardware, but MS and Intel getting into hardware, Amazon getting into hardware, Google buying Moto, this is all vertical integration  How can you support the idea that this trend will be reversed with no real justification? I'm sure mobile chips will continue to specialize, but I don't think this means what you think it means  Automobile companies started making their own engines and with rare exceptions, never went back to being more horizontal  Same with retail and their store brands  Same with cloud companies and their servers  Same with mobile companies and their OSs  The horizontal market of PCs created by long-lasting standards and loose hegemony is the exception, not the norm Yea, each year Amazon, MS, Apple and Google look more and more the same 
Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Intel's called Chipzilla for a reason up
Lagrange wrote:The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art I think the processing is a bigger advantage than many realize  If Intel can stay ahead in process design - which this article seems to indicate - they should have a major advantage  All else being equal a 14nm chip should be significantly faster and more efficient than the same chip at 22nm  Add in the fact that yields increase geometrically - you can fit a lot more 14nm chips on a given wafer size vs 22nm (or 32nm for the other manufacturers ) and you have a very appealing proposition  And then add in the fact that Intel actually has a pretty good graphics stack and IP  It's not a sure thing by any means, but I suspect ARM may have just prodded a sleeping giant edit: Also worth noting, Intel, TSMC, and Samsung are the only manufacturers who are building out 450nm wafers  This will increase yields dramatically  Of course Samsung and TSMC will build ARM out, but it definitely puts quite a bit of pressure on all other manufacturers  As the article mentions Intel and Samsung are the only ones who control production top to bottom, and Samsung must share some of the benefits with ARM 
As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP 
Last edited by paul5ra on Wed Feb 13, 2013 11:06 am
introiboad wrote:I am happy to see Kanter here at Ars, I like his writing and he maintains Real World Tech, where Linus Torvalds often shows up to comment on CPU arch and other interesting topics Indeed  Most tech writing in this area is atrocious  This piece is one of the few well informed articles I've read in a long time 
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The word you're looking for is Haswell, as far as I know 
Mabsark
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product 
gypsumfantastic wrote:Why wouldn't the foundries be able close the process gap with Intel? Is it a matter of money? Scale?Probably a mix of a lot of things  One big thing was during this recession, Intel was the ONLY fab company that didn't scale back their R&D  That alone gave Intel a large advantage Intel has almost always been ahead  One of the reasons could be that Intel works with much higher margins than many of the commodity companies like Samsung and TSMC Outside of the P4 flop and some of the monopolistic abuses, Intel has typically been selling to high end customers that are willing to pay a premium for "the best" Intel has a large benefit of having a relatively "good name" when it comes to CPUs, so they can effectively charge a brand-name premium I'm sure there are other reasons, and probably better reasons, but these are the main ones that I think of 
Mabsark wrote:Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product That's true as long as most people are still buying both a tablet and a laptop when each needs to be replaced  I think the assumption is that, as you say, the tablet market will saturate, with people just replacing existing ones, but the desktop/laptop market could decrease much farther than that, if most people stop replacing them at all  I'm not sure of the likelihood of that, but I think that's where this idea comes from 
ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The upcoming Haswell chip is showing to consume 1/3 the power of IvyBridge at peak, consumes 1/20th the power at idle, all the while maintaining Identical or better performance This chip should actually compete with ARM CPUs on both power/performance and idle I am expecting a large war 
Apple once again is dictating the performance in the mobile industry  Nice to see others being able to keep the pace, as well 
paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple evolutionary path by the SoC providers since then Yeah, and most of the innovation in the automobile industry came about before Henry Ford came into the business  Doesn't change the fact that cars would probably have been an asterisk in the history books under "toys for rich people" if it weren't for him The same applies to to mobile computing for Apple, Samsung, et al 
SheldonRoss wrote:Lagrange wrote:The question for the future is how the economics will stack up when overall device costs fall significantly and there is a big downward pressure on SoC prices  In that situation, can Intel still justify bringing their A-game to a market where products are essentially commoditised and you have processors selling for a only a few dollars each?The lesson from their previous involvement in the DRAM market is that they probably won't want to be involved because there isn't enough money to be made to justify manufacturing phone SoCs on a cutting edge, or near cutting edge process  In that scenario, Intel may not totally abandon the market but they might just stick to manufacturing SoCs on nodes that are a step or two behind the state of the art I think the processing is a bigger advantage than many realize  If Intel can stay ahead in process design - which this article seems to indicate - they should have a major advantage  All else being equal a 14nm chip should be significantly faster and more efficient than the same chip at 22nm  Add in the fact that yields increase geometrically - you can fit a lot more 14nm chips on a given wafer size vs 22nm (or 32nm for the other manufacturers ) and you have a very appealing proposition  And then add in the fact that Intel actually has a pretty good graphics stack and IP  My point was that Intel might have a one or two process advantage over the rest of the industry at the cutting edge but that doesn't mean that they can afford to manufacture on those processes for very low margin parts  If the SoC market becomes increasingly commoditised, there isn't going to be the money to justify making them in a state of the art fab Remember that one of the big selling points of Itanium was that it would make use of process advantages that were effectively paid for by the mainstream x86 market  That didn't quite work out in practice and Itanium processors were often well behind Xeons in process technology 
paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM 
Last edited by melgross on Wed Feb 13, 2013 11:13 am
Mark Havel wrote:ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that The word you're looking for is Haswell, as far as I know If tablets move into the $100-200 range, is there going to be room for Haswell?So long as there is a higher-end tablet market, then Haswell will be able to shine, but it's going to be a much more powerful and costly part than the sort of ARM based hardware that often runs tablets  If we see a race to the bottom where price is the dominant motivator behind purchases, then a high performance SoC will struggle to make its mark 
melgross wrote:paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM Of course I realise ARM IP has indeed been a major driving factor too (though only one if several architectures before ARM became dominant), though I see ARM's influence on the mobile industry as having nothing to do with modern day Apple and only one small piece of the puzzle  My point is that the hard electrical engineering, mathematics, DSP, semiconductor physics/chemistry, RF engineering, analogue design, CAD etc  that make modern telecommunications possible has very little to do with the fashion companies who consumers (and unfortunately much of the tech media) associate with it and give the credit (though in this respect Samsung does deserve a bit more credit for their work on NAND flash and displays)  The industry simply would not exist TODAY without the overwhelming horizontal integration that already dominates 
Quote:In the long term, mobile devices are likely to evolve similarly to the PC and favor a horizontal business model  The real advantage is one of flexibility; as costs drop and the market expands, it will be increasingly necessary for vendors like HTC to offer a wide range of phones based on radically different SoCs  You don't mention in the article that each SoC necessarily requires a bit of parallel dev work unlike the PC  In the PC world there is a standard BIOS and HW architecture that allows for pluggable designs  On a highly integrated SoC this is untrue  HTC suffers because it has to support radically different SoCs, their drivers and boot loaders, etc  Quote:While a vertically integrated company like Apple can focus and maintain leadership in a specific (and highly lucrative) niche, it would be very difficult to expand in many growing areas of the market  The differences between an iPhone 6 and a $20 feature phone are tremendous and would be very difficult for a single company to bridge It's only difficult because Apple chooses to ignore that market, not because they can't  If they can release a $99 Apple TV, they can surely cobble together a $20 feature phone if they chose to eschew 8GB of NAND, BT, WiFi, a specialized dock connector, LTE, and their specialized processors  In other words, build the equivalent of an iPod shuffle with a horrible screen and no OS to speak of 
paul5ra wrote:melgross wrote:paul5ra wrote:As someone who has worked in the semiconductor industry for longer than contemporary fanboys have existed, I'm getting a bit fed-up seeing many of these articles which rewrite history with analyses distorted by the lens of the contemporary Apple or Samsung fanboy The mobile industry moved to horizontal integration a long time ago  Better indicators than these odd contemporary obsessions with the relatively non-innovative Samsung and Apple where when Motorola spun out its semiconductor division as Freescale, Nokia stopped making it's own custom designs with TI and ST, and Ericsson spun out it's Ericsson Mobile Platforms division and formed ST-Ericsson with ST The true innovation in the mobile market was done a decade or more ago mainly by Moto/Nokia/Ericsson/TI/Qualcomm, and Samsung and Apple had little to do with it  Under the hood most stuff has been on a simple linear evolutionary path by the SoC providers since then  The phone manufacturers have then mainly been simply sticking these off-the-shelf SoCs (and their included low-level software stacks) in a box, a job made all the easier with the SoC manufacturer collaboration providing the bulk of the work for the AOSP Just goes to show that people who have worked in an industry for a long time don't always understand what that industry is doing You haven't been working in it long enough to seem to know that it was Acorn and Apple that invented the mobile ARM CPU in the first place  All those companies you've mentioned have just been working off Acorn and Apple's pioneering work  Now, Apple is back at it again, very successfully, and all the companies you mentioned that produce chips with ARM IP in them are licensing them from the company Acorn and Apple formed—ARM Of course I realise ARM IP has indeed been a major driving factor too (though only one if several architectures before ARM became dominant), though I see ARM's influence on the mobile industry as having nothing to do with modern day Apple and only one piece of the puzzle  My point is that the hard electrical engineering, mathematics, DSP, semiconductor physics/chemistry, RF engineering, analogue design,etc  that make modern telecommunications possible has very little to do with the fashion companies who consumers (and unfortunately much of the tech media) associate with it and give the credit (though in this respect Samsung does deserve a bit more credit for their work on NAND flash and displays)  The industry simply would not exist TODAY without the overwhelming horizontal integration that already dominates Yes the efforts of these companies getting cellular communications standardized were immense  And the technology matured  And then they didn't do much with it  It took some youngin's to look at the problem fresh and add the UI that make today's smartphones work  As we have all seen, the moment your technology has matured is the moment you are screwed because someone else now has the opportunity to look at it as a black box and make something new  Each of those manufacturers knew that smartphones would eventually be awesome, but none of them had the UI and software design to make a truly breakout product  Imagine if Motorola would have been smart enough to buy the Android guys instead of Google  Instead, Google bought a bunch of patents on that cellular black box to try to defend it's platform And when you think about it, which consumes more man years of engineering effort per year at this point     iterating that cellular black box or developing the OS, services and apps that power today's smartphones?
Intel had better decide that they are competing in this space "for real", or they are screwed  They've already let the Atom languish for five years, during which ARM has completely caught up in performance Just like Tim Cook said, if you don't cannibalize your own markets someone else will do it for you Whether Intel will embrace that concept in time remains to be seen  Personally, I hope they don't; if Intel transforms into a chipless Fab company (like TSMC) everyone benefits 
I still think Samsung has the advantage long term because they have both the SOC and the memory products  As mentioned in the article, TSV's (Through Silicon Via's) are going to be quite a disruption  Today, people normally stack an LPDDR2 package on top of their SOC package (POP or Package On Package)  Within the LPDDR2 package, you could have a stack of DRAM die typically with wire bonding connecting the die within the package Once you more to TSV's, you can have a LOT more connections between the SOC and its DRAM's  While this is being standardized through JEDEC (http://www jedec org/category/technolog     a/3d-ics-0), Samsung has all the pieces in house to do whatever they want  You could see a 512 bit or higher bus from the SOC to the memory  The trick is that the memory and the SOC need to line up with each other when you stack them  This gives Samsung an inherent advantage This isn't just going to impact mobile either  Take a look at that JEDEC link  It also lists High Bandwidth Memory (HBM)  This is a 1024 bit bus that provides 128GBytes/s to 256GBytes/s of bandwidth to a stack of up to 8 DRAM's  Here is your processor that includes 8-16 cores and 4GBytes of really, really, fast DRAM    No DIMMs required  How many of them do you want in your server rack?If I was Intel or Apple, I would be thinking seriously about making some investments in Micron to guarantee they make some compelling DRAM's to integrate with their SOC's and processors    otherwise Samsung is going to blow them out of the water on bandwidth 
Great_Scott wrote:Intel had better decide that they are competing in this space "for real", or they are screwed  They've already let the Atom languish for five years, during which ARM has completely caught up in performance Just like Tim Cook said, if you don't cannibalize your own markets someone else will do it for you Whether Intel will embrace that concept in time remains to be seen  Personally, I hope they don't; if Intel transforms into a chipless Fab company (like TSMC) everyone benefits It's true that Atom has stood still for too long, but honestly it's pretty amazing how Atom is still competitive with current ARM chips  The Z2760 is even 32nm vs 28nm of the latest Krait and A15 chips But that's all changing with Atom moving to the tick tock schedule this year  It wouldn't even surprise me to see Apple move to Intel chips for IOS And I don't see how Intel moving to a chipless Fab company would help everyone  It certainly wouldn't help Intel 
Mabsark wrote:ggeezz wrote:Intel cannot abandon the phone/tablet market  Desktop/laptop sales are stagnating/decreasing and phones/tablets are on the rise  This trend is only going to increase going forward But you're right, they're going to have use their fabs that are a step or two behind the cutting the edge  But they're going to have to up their game in the tablet space to even be able to do that Actually, that trend will not simply keep increasing going forward  The reason desktop/laptop sales are stagnating/decreasing is due to the fact that most people already have one and therefore don't need to buy another one  The exact same thing will happen with tablets as well  Sales are increasing now because people without tablets are buying them  When most people already own a tablet, they won't be buying a new one every year and therefore sales will stagnate/decrease The PC market is saturated and in a couple of years, the tablet market will be saturated too  Basically, in order to increase sales in a saturated market, you need to increase the population growth or decrease the longevity of the product Yes and no  I'm not sure the tablet market will saturate in a "couple of years " It may be more like 5 years  But that's a quibble Here's the real issue  Right now Apple wants you to own an iPhone AND iPad AND Macbook AND iWatch AND Apple TV  Microsoft, OTOH, is making the Surface so that you could ditch your laptop and just use a Surface  Not everyone, but some people If 5 years from now, we're in a world where a significant number of people use a Surface-type device instead of a laptop, then the PC market is going to contract significantly  Maybe some of the tablet-like devices will use moderately expensive Intel chips, but some of them are going to use cheaper chips 
GravyGraphics wrote:I still think Samsung has the advantage long term because they have both the SOC and the memory products  As mentioned in the article, TSV's (Through Silicon Via's) are going to be quite a disruption  Today, people normally stack an LPDDR2 package on top of their SOC package (POP or Package On Package)  Within the LPDDR2 package, you could have a stack of DRAM die typically with wire bonding connecting the die within the package Once you more to TSV's, you can have a LOT more connections between the SOC and its DRAM's  While this is being standardized through JEDEC (http://www jedec org/category/technolog     a/3d-ics-0), Samsung has all the pieces in house to do whatever they want  You could see a 512 bit or higher bus from the SOC to the memory  The trick is that the memory and the SOC need to line up with each other when you stack them  This gives Samsung an inherent advantage This isn't just going to impact mobile either  Take a look at that JEDEC link  It also lists High Bandwidth Memory (HBM)  This is a 1024 bit bus that provides 128GBytes/s to 256GBytes/s of bandwidth to a stack of up to 8 DRAM's  Here is your processor that includes 8-16 cores and 4GBytes of really, really, fast DRAM    No DIMMs required  How many of them do you want in your server rack?If I was Intel or Apple, I would be thinking seriously about making some investments in Micron to guarantee they make some compelling DRAM's to integrate with their SOC's and processors    otherwise Samsung is going to blow them out of the water on bandwidth Why not AMD? Last I checked they still made memory   and processors/GPUs 
Context 3: Paper Info

Title: Interpretable reduced-order modeling with time-scale separation Interpretable reduced-order modeling with time-scale separation
Publish Date: 7 March 2023
Author List: Sebastian Kaltenbach (from CSE-Lab, ETH Zurich, Harvard SEAS), Phaedon-Stelios Koutsourelakis (from CSE-Lab, ETH Zurich, Harvard SEAS), Petros Koumoutsakos (from CSE-Lab, ETH Zurich, Harvard SEAS), Harvard Seas (from CSE-Lab, ETH Zurich, Harvard SEAS)

Figure

FIG  5  Comparison between the phase-space of the reference solution (left) and the phase-space of the predictions
FIG  7  Comparison between predictions and reference solutions for a new initial condition fort = 1 25, 3 75, 7 5, 12 5, 20, 30  (from left to right and top to down) We note that with longer prediction time the uncertainty bounds increases Despite the chaotic nature of the KS equation, the predictive posterior mean is close to the reference solution for t ≤ 12 5

abstract

Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering  However, finding solutions for these PDEs can be computationally expensive, making model-order reduction crucial  We propose such a data-driven scheme that automates the identification of the time-scales involved and, can produce stable predictions forward in time as well as under different initial conditions not included in the training data 
To this end, we combine a non-linear autoencoder architecture with a time-continuous model for the latent dynamics in the complex space  It readily allows for the inclusion of sparse and irregularly sampled training data  The learned, latent dynamics are interpretable and reveal the different temporal scales involved 
We show that this data-driven scheme can automatically learn the independent processes that decompose a system of linear ODEs along the eigenvectors of the system's matrix  Apart from this, we demonstrate the applicability of the proposed framework in a hidden Markov Model and the (discretized) Kuramoto-Shivashinsky (KS) equation 
Additionally, we propose a probabilistic version, which captures predictive uncertainties and further improves upon the results of the deterministic framework 

INTRODUCTION

High-fidelity simulations of critical phenomena such as ocean dynamics and epidemics have become essential for decision-making  They are based on physically-motivated PDEs expressing system dynamics that span multiple spatiotemporal scales and which necessitate cumbersome computations   In recent years there is increased attention to the development of data-driven models that can accelerate the solution of these PDEs as well as reveal salient, lower-dimensional features that control the long-term evolution 
In most cases, data-driven reduced-order models are not interpretable  In particular, models based on neural networks despite good predictive capabilities , they offer a black-box description of the system dynamics  A possible remedy is applying a symbolic regression to the learned neural network representation , but this adds additional computational cost due to the two-step procedure 
A number of frameworks such as SINDy allows to learn interpretable dynamics but it relies on the a-priori availability of lower-dimensional descriptors and of time-derivatives which can be very noisy for both simulation and experimental data  Other frameworks are tailored to specific problems such as molecular dynamics  
Here, we present a framework that only needs the value of the observables, and not their derivatives, as training data and is capable of identifying interpretable latent dynamics  The deployment of interpretable latent dynamics ensures that conservation of important properties of that are reflected in the reduced-order model  
The present method is related to approaches based on the Koopman-operator extended Dynamic Mode Decomposition (eDMD) but uses continuous complex-valued latent space dynamics and only requires one scalar variable per latent dimension to describe the latent space dynamics  Therefore we do not have to enforce any parametrizations on the Koopman matrix  
The time-continuous formulation moreover allows to incorporate sparse and irregularly sampled training data and fast generation of predictions after the training phase  By using a complex-valued latent space we can also incorporate harmonic effects and reduce the number of latent variables needed  Linear and non-linear autoencoders are used to map the observed, high-dimensional time-series to the lower-dimensional, latent representation and we identify simultaneously the autoencoder as well as the latent dynamics by optimizing a combined loss function 
Hence the to tasks of dimensionality reduction and discovery of the reduced dynamics are unified while other frameworks treat the two parts separately   Apart from using an architecture based on autoencoders to identify the latent space, projection-based methods could also be employed   We are also proposing a probabilistic version of our algorithm ) that makes use of probabilistic Slow Feature Analysis  
This allows for a latent representation that arart from being time-continuous, can quantify the predictive uncertainty and hierarchically decompose the dynamics into their pertinent scales while promoting the discovery of slow processes that control the system's evolution over long time horizons  The rest of the paper is structured as follows: We introduce the methodological framework as well as algorithmic details in section II 
Particular focus is paid on the interpretability of the inferred lower-dimensional dynamics  In section III we present three numerical illustrations, i e  a system of linear ODEs, a hidden Markov Model and the discretized KS-equation  We then present in section IV the probabilistic extension of the framework and apply it to the KS-equation 
We conclude with a summary and a short discussion about possible next steps  We introduce the autoencoders deployed in this work, followed by the interpretable latent space dynamic and discuss the training process  We consider data from high-dimensional time series x n ∈ R f with n = 1,   



ground_truth: Margaret Way was born in Brisbane and died in Cleveland, Queensland, Australia.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How are smartphones and tablets different from a technical perspective?

Read the following text and answer briefly.

Context 3: , T   We remark that the intervals between the different states do not need to be uniformly spaced 

Autoencoder

A core assumption of the method is that each high-dimensional state x n can be compressed to a lower-dimensional representation z n ∈ C c with c << f   We identify this lower-dimensional representation by an autoencoder consisiting of a parameterized encoder and decoder  The encoder maps the high-dimensional representation to the latent space as:
The latent space is complex-valued  The decoder reconstructs the high-dimensional representation based on the latent variables as: We denote the parameters of the encoder as well as the decoder by θ  As discussed later in Section II C, both set of parameters are optimized simultaneously during training and therefore there is no need for differentiating them 

Interpretable Latent Space Dynamics

We employ a propagator in the latent space to capture the reduced-order dynamics of the system  In contrast to other time-extended variational autoencoder frameworks, our representation uses complex valued latent variables  In addition the latent variables are treated independently  The latter feature enables us to have an interpretable latent dynamics as well as a model that is especially suitable for being trained in the Small Data regime due to the small number of required parameters 
This is in contrast to temporal propagators such as LSTMs   For each dimension i of the latent variable z we are using the following continuous ODE in the complex plane: By solving this ODE, we can define the operator: Interpretable reduced-order modeling with time-scale separation Here, λ is a vector containing all the individual λ's and ∆t n indicates the time-step between the latent states 
The symbol is used to indicate a component-wise multiplication  We remark that the latent variables and the parameter governing the temporal evolution are complex numbers and their role in describing the system dynamics is similar to that of an eigenvalue  The real part is associated with growth and decay whereas the imaginary part is representing the periodic component 
This approach has similarities with the Koopman-operator based methods and the extended dynamic mode decomposition   In contrast to the methods mentioned before we are using a continuous formulation in the latent space that allows us to incorporate scarce and irregularly sampled training data and directly rely on complex numbers in the latent space 

Training and Predictions

We optimize a loss function that combines both a reconstruction loss as well as a loss associated with the error of our learned propagator in the latent space: (5) We note that we could directly incorporate mini-batch training by only taking the summation over a subset of the N available training data 
For new predictions of unseen states, we use the encoder to generate a latent representations which is then advanced in time by the learned propagator  At a designated time step we are using the decoder to reconstruct the high-dimensional solution  We applied our algorithm to three systems  First, we show that the algorithm is capable of exactly reproducing the solution of a linear ODE and to identify its eigenvalues 
Afterwards we are applying the framework to a high-dimensional process generated by a complex latent dynamics, which is correctly identified  As a final test case, we are applying the algorithm to a Kuramoto Shivashinski (KS) equation  Interpretable reduced-order modeling with time-scale separation

Linear ODE

We are considering a two-dimensional ODE system for x = y 1 y 2 : Based on the obtained training data we run our algorithm using a linear encoder and decoder structure as well as two latent variables z  The loss function was optimized using the Adam algorithm   As we consider a linear ODE we can analytically compute the eigenvalues involved and compare it with the parameters λ identified by our algorithm 
We observe in Figure that the algorithm was able to recover the correct values, i e  the eigenvalues 7 and 3 of the given linear ODE  The system does not have a periodic component and the two imaginary parts correctly go to zero, whereas the real parts converge to the reference value  Moreover we are also able to identify for the linear mapping between our latent variables z and the training data a matrix consisting of a multiple of the eigenvectors (1,1) and (1,-1) and thus the correct solution 
This example was chosen to show that the algorithm is able to quickly identify the exact solution of a linear ODE in terms of its linearly independent components 

Hidden multiscale dynamics

We consider eight-dimensional synthetic time series data produced by an underlying twodimensional complex valued process  In particular, the data points x are generated by first solving for the temporal evolution for the two complex-valued processes p 1 and p 2 and than mapping to the eight-dimensional space by using a randomly sampled linear mapping W  
One of the two processes used to generate the data is chosen to be much slower than the other one and both processes have a periodic component  dp 2 dt = (−0 9 + 1 5i)p 2 (8) As training data we consider 40 time series with 150 data points each, obtained by simulating the described processes for a maximum of t = 15 s and then sampling from the obtained data points 
Hence the training data consists of: • 40 time-series • with each consisting 150 observations of the x at a uniform time-step ∆t = 0 0025 The autoencoder obtained consists of one linear layer for both the decoder as well as the encoder  The model is trained for 5000 iterations using the Adam optimizer and a learning rate of 10 −3  
The results for the convergence of the parameters λ 1 and λ 2 can be found in Figure   We note that the process which is slower decaying and thus more responsible for the long-term evolution of the system has a higher convergence rate than the faster process  With the obtained parameters λ as well as the trained autoencoder, we compute predictions based on the last time step used for training, i e  we apply the encoder to obtain our latent representation and than use the latent dynamics to advance the latent representation in time 
Afterwards, we employ the decoder to reconstruct the full high-dimensional system  The results can be found in Figure and show very good agreement between predictions and reference data



ground_truth: Smartphones are more compact and power constrained.

prompt_front: Now, answer the following question based on the text below, only give me the answer and do not output any other words.

Question: How does the framework capture the reduced-order dynamics?

Read the following text and answer briefly.

Context 3:  This example shows that our model is successfully able to carry out dimensionality reduction and moreover indicates that the convergence rate between latent processes can be different 
The latter is relevant when training models as for accurate predictions all latent processes and their dynamics should be converged 

Kuramoto-Sivashinsky

Finally, we applied our algorithm to the KS equation and aim to identify a reduced-order model for the solution u(y, t): We employed periodic boundary conditions, µ = 1 and a domain size y ∈ [0, 22]  For this domain-size, the KS-equation exhibits a structurally stable chaotic attractor as discussed in The black lines divides the area for which training data was given from the area without raining data 
;   The equation is discretized in space using a discretization step of 22 64 resulting in a state vector x of dimension 64 and a nonlinear system of coupled ODEs  This is solved using a stiff fourth-order solver  We employed a non-linear encoder and decoder with four fully-connected layers each and ReLU-activation functions as well as Dropout Layers between the fully-connected layers 
We trained the model for 200000 iterations using Adam and a learning rate of 5 • 10 4 and assuming a five-dimensional latent space  We obtained the λ's in Figure   Four latent variables have λ's close to zero and thus a slow temporal dynamic that is responsible for the long-term evolution whereas one latent variable is quickly decaying 
Based on the obtained parameters, we do predictions based on an unseen initial condition not contained in the training data  We are able to reconstruct the correct phase space based on our predictions despite only using a very limited amount of training data  The results for the phase space can be seen in Figure  
Although the small-scale fluctuations in the temporal dynamics are not well captured, the model identifies the correct manifold which has a good accuracy compared to the reference solution  All phase-spaces were obtained by using a finite-difference operator on the data or predictions  These results are in accordance Interpretable reduced-order modeling with time-scale separation with whose LSTM-based temporal dynamic model was also able to find the correct phase space but not to track the actual dynamics for long-term predictions 
Our model is not able to account for noise in the temporal evolution and thus dealing with chaotic, small-scale fluctuations is challenging  We believe that a probabilistic version of our algorithm could be advantageous here  This section contains a fully probabilistic formulation for the deterministic model discussed before 
We replace the Autoencoder with a Variational Autoencoder and the ODE in the latent space with a SDE  The loss function which we optimize is the Evidence-Lower Bound (ELBO) 

Model Structure

We postulate the following relations for our probabilistic model using an Ornstein-Uhlenbeck (OU) for each dimension i of the latent space and a Wiener process W t in the latent space: We again assume that the latent variables z t are complex-valued and a priori independent  Complex variables were chosen as their evolution includes a harmonic components which are observed in many physical systems 
We assume an initial conditions z 0,i ∼ CN (0, σ 2 0,i )  The total parameters associated with the latent space dynamics of our model are thus {σ 2 0,i , σ 2 i , λ i } c i=1 and will be denoted by θ together with all parameters responsible for the decoder mapping G (see next section)  These parameters along with the state variables z t have to be inferred from the data x t  
Based on probabilistic Slow Feature Analysis (SFA) , we set σ 2 i = 2; (λ j ) and σ 2 0,i = 1  As a consequence, a priori, the latent dynamics are stationary  A derivation and reasoning for this choice can be found in Appendix A  Hence the only independent parameters are the λ i , the imaginary part of which can account for periodic effects in the latent dynamics 

Variational Autoencoder

We employ a variational autoencoder to account for a probabilistic mappings from the lower-dimensional representation z n to the high-dimensional system x n   In particular we are employing a probabilistic decoder The encoder is used to infer the state variables z based on the given data and thus defined in the inference and learning section 

Inference and Learning

Given the probabilistic relations , our goal is to infer the latent variables z 0:T as well as all model parameters θ  We follow a hybrid Bayesian approach in which the posterior of the state variables is approximated using amortized Variational Inference and Maximum-A-Posteriori (MAP) point-estimates for θ are computed 
The application of Bayes' rule for each data sequence x 0:T leads to the following posterior: where p(θ) denotes the prior on the model parameters  In the context of variational inference, we use the following factorization of the approximate posterior i e  we infer only the mean µ and variance σ for each state variable based on the given data points 
This conditional density used for inference is the encoder-counterpart to the probabilistic decoder defined in the section before  It can be readily shown that the optimal parameter values are found by maximizing the Evidence Lower Bound (ELBO) F(q φ (z 0:T ), θ) which is derived in Appendix B  We compute Monte Carlo estimates of the gradient of the ELBO with respect to φ and θ with the help of the reparametrization trick and carry out stochastic optimization with the ADAM algorithm  

Results for the probabilistic extension

We applied our probabilistic version to the KS-equation  We used the same settings as for the deterministic approach but considered up to 10 complex latent variables  The obtained λ's are in Figure   The probabilistic model allows us to quantify the uncertainty in predictions  In Figure predictions for various time-steps and the respective uncertainty bounds are shown for an unseen initial condition 
Due to the chaotic nature of the KS-equation and the small amount of training data, the underlying linear dynamic of our model is only able to capture the full dynamics for a limited time horizon  Fortunately, due to the probabilistic approach the model is capable of capturing chaotic fluctuations with increasingly wide uncertainty bounds 
We also computed the phase space representation for the KS-equation based on the predictions obtained by our model and compare it with the reference solution  The probabilistic model identifies the correct manifold with a better accuracy than the deterministic model  As some of the small-scale fluctuations are accounted as noise, the resulting manifold is more concentrated at the origin and the obtained values are slightly smaller than the reference manifold although their shape is very similar 



ground_truth: By using a propagator in the latent space.