Physics-ML 開発のためのフレームワーク
NVIDIA Modulus の紹介
Naruhiko Tan, Solution ArchitectAgenda•What is NVIDIA Modulus•

Use cases•

What’s new and online resources

What is NVIDIA Modulus

Getting started with ai for engineering simulations using modulus onrescale platform [S42087]
NVIDIA MODULUS
Framework for Developing Physics ML Models for Digital Twins Use simulation and observation data and governing physics
equations to generate a robust surrogate model Generalizes parameterized domain and physics to encapsulate
multiple configurations/scenarios in the trained model Builds a Physics ML model/digital twin to iterate on thedesign/operating space Forward simulation, inverse and data assimilation problems

 What its not? Not a Solver, Not a Simulation platform

Developing digital twins for weather, climate, and energy [S41823]

Physics-ML categorization
Fully data
drivenData

Inductive
bias

Physics
constrained

Fully physics
drivenPhysics

12

NVIDIA Modulus – A Framework
Key concepts

Specifying geometry of the domain

Network architectures – Curated networks• STL or Constructive Solid Geometry (CSG)• Fourier Features (FN), Sinusoidal Representation(SiReNs), Modified Fourier Features (mFN)• Specify sampling policy• Specify parameterization• Fourier Neural Operator, Adaptive Fourier NeuralOperator• Fully Connected (FC)• Deep Galerkin Method (DGM)

Using ground truth data in Modulus• Modified Highway Networks• Observed data or simulation data

• Multiplicative Filter Networks• Use only the governing equations with no dataand more…

• Use only data
• Use both
• Consistent with first principles• Faster convergenceCase Study on Developing Digital Twins for the Power Industry usingModulus and Omniverse [S41671]
NVIDIA MODULUS ² A FRAMEWORKKey ConceptsSpecify governing equations
 Symbolic equations
 Integral form or weak form

 extensible

Loss function minimization
 Satisfy the PDE
 Boundary conditions

Case Study on Developing Digital Twins for the Power Industry using
Modulus and Omniverse [S41671]
NVIDIA MODULUS ² A FRAMEWORKKey Concepts

Specify governing equations
 Symbolic equations
 Integral form or weak form

 extensible

Loss function minimization
 Satisfy the PDE
 Boundary conditions

Explicit Parameterization

S41823: Towards developing digital twins for weather, climate, and energy

MODULUS
FRAMEWORKVERIFICATION
Modulus Framework - Verification
CFD

Solid Mechanics

Acoustics

Laminar

Turbulent

15

MODULUS
FRAMEWORKVERIFICATIONMODULUSFRAMEWORKVERIFICATION
Modulus Framework - Verification
Electromagnetics
Electromagnetics

Vibrations
Vibrations

Turbulence
Turbulence

Modulus
Modulus

Modulus
Modulus

Modulus
Modulus1616

Modulus Framework - Verification
Taylor-Green Vortex Decay

Modulus Framework - Performance
SINGLE GPU: Tensor Core Speed-Up for PDEs

A100 FP32 vs. TF32: Results, Compute Time, Loss

Modulus Framework - Performance
MULTI-GPU: Node Scalability

AI IN AISCIENCE&ENGINEERINGin Science and Engineering
Improved Physics & Predictions

14

Use cases• Reacting flow in industrial scale boiler• Fluid accelerated corrosion of heat recovery
steam generator

Developing Digital Twins for Energy Applications using Modulus[S41325]

PINN for reacting flows
Formulation and PINN vs CFD

 Aim: Create a digital twin of an industrial scale boiler
 Simplified methane oxidation
 Implemented reacting flow transport equations for
kinetics-controlled combustion
 No requirement for training data
մ Single PINN model for a range of input conditions
մ Fidelity and accuracy comparable to CFD
մ Trained PINN can provide near-instantaneousinference for any input condition
Figure source: https://commons.wikimedia.org/wiki/File:Steam_Generator.png

7Developing Digital Twins for Energy Applications using Modulus[S41325]

Towards a reacting flow solver
Governing equations: Strongly coupled PDEs







Single species
Turbulent
Steady state
2D




Multiple species
Turbulent
Steady state
2D

Continuity:






డఘ

൅
డ௧
డ௒ೖ

డሺఘ௨೔ ሻడ௫೔Species mass fraction:

ߩMomentum:డሺఘ௨೔ ሻTemperature:డ்Kinetics-controlled single step irreversible reaction









Multiple species
ReactingTurbulentSteady state2Dడ௧డ௧൅ ߩ‫ݑ‬௜൅డ

Multiple species
Reacting
Turbulent
Transient
2D

Multiple species
Reacting
Turbulent
Transient3DൌͲడ௒ೖడ௫೔డሺఘ௨೔ ௨ೕ ሻడ௫ೕడൌ ߱௞ሶ +డ௫೔ߩ‫ܦ‬௞డ௣డఛ೔ೕ೔ೕൌ െ డ௫ ൅ డ௫ఠ ሶ೅డ೛డ௒ೖడ௫೔

డ்൅‫ݑ‬ܶൌ൅ߙ௝డ௧డ௫ఘ௖
డ௫డ௫೔
೔೔‫ܪܥ‬ସ ൅ ʹሺܱଶ ൅͵Ǥ͹͸ܰଶሻ ՜ ‫ܱܥ‬ଶ ൅ ʹ‫ܪ‬ଶܱ ൅ ͹Ǥͷʹܰଶఘ௒಴ಹర

ఘ௒ೀమ



Species source/sink terms߱஼ுସሶ ൌ െ‫ܹܯ‬஼ுସ ݇௙ ሺ

Temperature source termேேே଴்߱ሶ ൌ െ σ௞ୀଵ ݄௞ ߱ሶ௞ ൌ െ σ௞ୀଵ ݄௦௞ ߱௞ሶ െ σ௞ୀଵ ȟ݄௙ǡ௞ ߱௞ሶெௐ಴ಹరሻ ሺெௐೀమሻ etc8

Developing Digital Twins for Energy Applications using Modulus[S41325]

Simplified systems

PINN vs CFD

Temperature distribution with frozen species

Species distributions for case without T source term
Ansys Fluent

REACTANT

Modulus

Ansys Fluent

Modulus

Ansys Fluent

ModulusPRODUCT

14

Developing Digital Twins for Energy Applications using Modulus[S41325]

Resolving the issue with large T-source

Handling large T-source T-source dominates the Y-source This can lead to imbalances between the backpropagatedgradientsA) Gradient normalization approach Attempts to remove the dominanceof any component of the global loss
function Dynamically assigns weights todifferent constraintsB) Transient approach Handles large source terms bylearning the change between
states instead of learning
everything at once Uses a moving time window
approach16

Use cases• Reacting flow in industrial scale boiler• Fluid accelerated corrosion of heat recovery
steam generator

Case Study on Developing Digital Twins for the Power Industry using
Modulus and Omniverse [S41671]
A typical Heat Recovery Steam Generator and some challenges
for Digitalization
Low Pressor Evaporator
 Mix of steam and liquidchanges with operations
 Area of evaporation changeswith operationsÎPoint of corrosion difficult topredictBut Thousands of pipes, nosensors
 Fluid dynamics depend ongeometry, only 2D drawings
available
Exhaust gas flow and temperatur

August 2021

7Unrestricted © Siemens Energy, 2021

Case Study on Developing Digital Twins for the Power Industry using
Modulus and Omniverse [S41671]
The Fluid Accelerated Corrosion Workflow

Current
process

Geometry : 2D

3D

Full 3D geometry from 2D drawing

CFD Model preparation

3D CFD operating conditions

Geometry preparation for CFD, meshgeneration (possible iterations)Different operating conditions for creating
reduced order model response surface

The challenge of the current approach:

Betterprocess?

August 2021

 Detailed simulation take months to prepare for one plant Costs exceed customer benefits
 Simplified data driven approaches do not determine the risk level inan acceptable manner

9
Unrestricted © Siemens Energy, 2021

Case Study on Developing Digital Twins for the Power Industry using
Modulus and Omniverse [S41671]
HRSG WORKFLOW WITH MODULUSCurrent process

Geometry : 2D

3D

Full 3D geometry from 2D drawing

New suggestedprocess
2D drawing

Convert 2D drawings tocenterline geometry(~0.5 day)

Geometry : 2D

3D

3D geometryfor Fluids

Centerlinegeometry< 0.5 hrUsing standard
CAD tools

CFD Model preparation

3D CFD operating conditions

Geometry preparation for CFD, meshgeneration (possible iterations)Different operating conditions for creating
reduced order model response surface

Case Study on Developing Digital Twins for the Power Industry using
Modulus and Omniverse [S41671]
HRSG WORKFLOW WITH MODULUS

Current process

Geometry : 2D

3D

Full 3D geometry from 2D drawing

New suggestedprocess

Geometry : 2D

CFD Model preparation

3D CFD operating conditions

Geometry preparation for CFD, meshgeneration (possible iterations)Different operating conditions for creating
reduced order model response surface

Model Training

3D

 Mesh free, fast point cloud generation

2D drawing

3D geometry
for Fluids

Centerlinegeometry

 Incompressible NS eqs
 Fourier feature neural network
Convert 2D drawings tocenterline geometry(~0.5 day)

< 0.5 hrUsing standard
CAD tools

Parameterized input velocity

Case Study on Developing Digital Twins for the Power Industry using
Modulus and Omniverse [S41671]
HRSG WORKFLOW WITH MODULUS
ABCSymbolic definition of equations‫ܝڄ׏‬ൌͲߩ‫ ܝ׏ ڄ ܝ‬ൌ െ‫ ݌׏‬൅ ߤ‫׏‬ଶ ‫ܝ‬Hyperparameter tuning and training

Defining network architecture
Fourier Feature NetworkPySDF OLEUDU\0RGXOXV·7HVVHOODWHG*HRPHWU\module, Optix for Sampling and SDF‫ ݏݏ݋ܮ‬ൌ ‫ܮ‬௉஽ா ൅ ‫ܮ‬஻஼Verification andValidation
Good match (in A,B,C):

Case Study on Developing Digital Twins for the Power Industry using
Modulus and Omniverse [S41671]
HRSG WORKFLOW WITH MODULUS

Current process

Geometry : 2D

3D

Full 3D geometry from 2D drawing

Suggestedprocess

2D drawing

Geometry : 2D

3D

3D geometry
for Fluids

Centerline
geometry

Convert 2D drawings tocenterline geometry(~0.5 day)

< 0.5 hr

3D CFD operating conditions

Geometry preparation for CFD, meshgeneration (possible iterations)Different operating conditions for creating
reduced order model response surface

Model Training

Infer new scenario

 Mesh free, fast point cloud generation

 Order of 10,000x speed up per scenario

 Incompressible NS eqs

 Order of seconds inference time vs 8 hr

 Fourier feature neural network
Using standard
CAD tools

CFD Model preparation

Parameterized input velocity

per CFD run

What’s New and Online ResourcesNVIDIA Omnivers Enterprise

Platform for Creating and Connecting Virtual Worlds
Nucleus

RTX Renderer

PortalDesigner, Creator,
Engineer Collaborators
USD

Physics

Materials

Path-Tracing

NVIDIA Core TechnologyAICase Study on Developing Digital Twins for the Power Industry using
Modulus and Omniverse [S41671]
MODULUS ² OMNIVERSE INTEGRATION

Modulus Extension in Omniverse

Interactiveexploration

Visualization Extension

Model inference

Model Outputs

Visualization
pipeline

Output Rendering Modulus Omniverse extension: enables importing outputs of Modulus trained model into a visualization pipeline for common output scenarios ex:
streamlines, iso-surface
 provides an interface that enables interactive exploration of design variables/parameters to infer new system behavior

New Features in NVIDIA Modulus v22.03• New network architectures• Fourie Neural Operator• Physics Informed Neural Operator• Adaptive Fourier Neural Operator• Deep-O Net• Modeling Enhancements• 2-eqn. Turbulence model• k<latexit sha1_base64="FULNvxR0CTA5RmKEYCXKafsNPCc=">AAAB+3icbVDLSgNBEOz1GeMr6tHLYhC8GHYlqMegF48RzAOSJcxOepMxszPLzKwYQn7Fi4giXv0Rb/6Nk2QPmljQUFR1090VJpxp43nfztLyyuraem4jv7m1vbNb2Nuva5kqijUquVTNkGjkTGDNMMOxmSgkccixEQ6uJ37jAZVmUtyZYYJBTHqCRYwSY6V7GMApvABCAhoYcJAgOoWiV/KmcBeJn5EiZKh2Cl/trqRpjMJQTrRu+V5ighFRhlGO43w71ZgQOiA9bFkqSIw6GE1vH7vHVum6kVS2hHGn6u+JEYm1Hsah7YyJ6et5byL+57VSE10GIyaS1KCgs0VRyl0j3UkQbpcppIYPLSFUMXurS/tEEWpsXHkbgj//8iKpn5X881L5tlysXGVx5OAQjuAEfLiACtxAFWpA4RGe4BXenLHz7Lw7H7PWJSebOYA/cD5/AIQQkYg=</latexit>✏, k<latexit sha1_base64="q+OthTPT4zzYsSYxJtVSkuO79OE=">AAAB93icbVDJSgNBEK1xjXGLevTSGAQvhhkJ6jHoxWMEs0AyhJ5OT9Kkl6G7RwhDfsSLBxe8+ive/Bs7yRw08UHB470qqupFCWfG+v63t7K6tr6xWdgqbu/s7u2XDg6bRqWa0AZRXOl2hA3lTNKGZZbTdqIpFhGnrWh0O/Vbj1QbpuSDHSc0FHggWcwItk4awgjO4Q0UCKAwANwrlf2KPwNaJkFOypCj3it9dfuKpIJKSzg2phP4iQ0zrC0jnE6K3dTQBJMRHtCOoxILasJsdvcEnTqlj2KlXUmLZurviQwLY8Yicp0C26FZ9Kbif14ntfF1mDGZpJZKMl8UpxxZhaYhoD7TlFg+dgQTzdytiAyxxsS6qIouhGDx5WXSvKgEl5XqfbVcu8njKMAxnMAZBHAFNbiDOjSAgIUneIFXb+w9e+/ex7x1xctnjuAPvM8fd2aQcQ==</latexit>! models with standard and Launder-Spalding wall functions• Exact boundary condition imposition• Training features• Support for new optimizers• 30+ optimizers• New algorithms for loss balancing• Grad Norm, Relative Loss Balancing with Random Lookback, and Soft Adapt• Sobolev (gradient-enhanced) training• Hydra Config• Post-processing

New Features in NVIDIA Modulus v22.07• New network architectures• Generalized DeepONet architecture• FourCastNet• Training features• L1-L2 Loss Decaying• Performance Enhancements• Meshless Finite Differentiation• Dataset Refactor• Tiny CUDA NN• CUDA Graphs• Geometry Module Refactor

Online Resource

NVIDIA Modulus Product Page
https://developer.nvidia.com/modulus
User Guide
https://docs.nvidia.com/deeplearning/modulus/index.html
NVIDIA Modulus Resource Center
https://resources.nvidia.com/l/en-us-modulus-pathfactory-explore-page
Physics Machine Learning のためのフレームワーク、NVIDIA Modulus 最新事情
https://medium.com/nvidiajapan/physics-machine-learning%E3%81%AE%E3%81%9F%E3%82%81%E3%81%AE%E3%83%95%E3%83%AC%E3%83%BC%E3%83%A0%E3%83%AF%
E3%83%BC%E3%82%AF-nvidia-modulus-%E6%9C%80%E6%96%B0%E4%BA%8B%E6%83%85-2734ea6b5ad4

NVIDIA GTC 2022
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