pwc-archive/papers-with-abstracts huggingface dataset:
Fast Constraint Screening for Multi-Interval Unit Commitment
Authors: Xuan He, Jiayu Tian, Yufan Zhang, Honglin Wen, Yize Chen
Date: 2023-09-12 00:00:00

Power systems Unit Commitment (UC) problem determines the generator commitment schedule and dispatch decisions for power networks based on forecasted electricity demand. However, with the increasing penetration of renewables and stochastic demand behaviors, it becomes challenging to solve the large-scale, multi-interval UC problem in an efficient manner. The main objective of this paper is to propose a fast and reliable scheme to eliminate a set of redundant or inactive physical constraints in the high-dimensional, multi-interval, mixed-integer UC problem, while the reduced problem is equivalent to the original full problem in terms of commitment decisions. Our key insights lie on pre-screening the constraints based on the load distribution and considering the physical feasibility regions of multi-interval UC problem. For the multistep UC formulation, we overcome screening conservativeness by utilizing the multi-step ramping relationships, and can reliably screen out more constraints compared to current practice. Extensive simulations on both specific load samples and load regions validate the proposed technique can screen out more than 80% constraints while preserving the feasibility of multi-interval UC problem.
The Safety Filter: A Unified View of Safety-Critical Control in Autonomous Systems
Authors: Kai-Chieh Hsu, Haimin Hu, Jaime Fernández Fisac
Date: 2023-09-11 00:00:00

Recent years have seen significant progress in the realm of robot autonomy, accompanied by the expanding reach of robotic technologies. However, the emergence of new deployment domains brings unprecedented challenges in ensuring safe operation of these systems, which remains as crucial as ever. While traditional model-based safe control methods struggle with generalizability and scalability, emerging data-driven approaches tend to lack well-understood guarantees, which can result in unpredictable catastrophic failures. Successful deployment of the next generation of autonomous robots will require integrating the strengths of both paradigms. This article provides a review of safety filter approaches, highlighting important connections between existing techniques and proposing a unified technical framework to understand, compare, and combine them. The new unified view exposes a shared modular structure across a range of seemingly disparate safety filter classes and naturally suggests directions for future progress towards more scalable synthesis, robust monitoring, and efficient intervention.
Ensemble-based modeling abstractions for modern self-optimizing systems
Authors: Michal Töpfer, Milad Abdullah, Tomáš Bureš, Petr Hnětynka, Martin Kruliš
Date: 2023-09-11 00:00:00

In this paper, we extend our ensemble-based component model DEECo with the capability to use machine-learning and optimization heuristics in establishing and reconfiguration of autonomic component ensembles. We show how to capture these concepts on the model level and give an example of how such a model can be beneficially used for modeling access-control related problem in the Industry 4.0 settings. We argue that incorporating machine-learning and optimization heuristics is a key feature for modern smart systems which are to learn over the time and optimize their behavior at runtime to deal with uncertainty in their environment.
Design and Validation of a Metallic Reflectarray for Communications at True Terahertz Frequencies
Authors: Sherif Badran, Arjun Singh, Arpit Jaiswal, Erik Einarsson, Josep M. Jornet
Date: 2023-09-11 00:00:00

Wireless communications in the terahertz band (0.1-10 THz) is a promising and key wireless technology enabling ultra-high data rate communication over multi-gigahertz-wide bandwidths, thus fulfilling the demand for denser networks. The complex propagation environment at such high frequencies introduces several challenges, such as high spreading and molecular absorption losses. As such, intelligent reflecting surfaces have been proposed as a promising solution to enable communication in the presence of blockage or to aid a resource-limited quasi-omnidirectional transmitter direct its radiated power. In this paper, we present a metallic reflectarray design achieving controlled non-specular reflection at true terahertz frequencies (i.e., 1-1.05 THz). We conduct extensive experiments to further characterize and validate its working principle using terahertz time-domain spectroscopy and demonstrate its effectiveness with information-carrying signals using a continuous-wave terahertz testbed. Our results show that the reflectarray can help facilitate robust communication links over non-specular paths and improve the reliability of terahertz communications, thereby unleashing the true potential of the terahertz band.
Robust Nonlinear Reduced-Order Model Predictive Control
Authors: John Irvin Alora, Luis A. Pabon, Johannes Köhler, Mattia Cenedese, Ed Schmerling, Melanie N. Zeilinger, George Haller, Marco Pavone
Date: 2023-09-11 00:00:00
Tasks: Dimensionality Reduction, model, Model Predictive Control

Real-world systems are often characterized by high-dimensional nonlinear dynamics, making them challenging to control in real time. While reduced-order models (ROMs) are frequently employed in model-based control schemes, dimensionality reduction introduces model uncertainty which can potentially compromise the stability and safety of the original high-dimensional system. In this work, we propose a novel reduced-order model predictive control (ROMPC) scheme to solve constrained optimal control problems for nonlinear, high-dimensional systems. To address the challenges of using ROMs in predictive control schemes, we derive an error bounding system that dynamically accounts for model reduction error. Using these bounds, we design a robust MPC scheme that ensures robust constraint satisfaction, recursive feasibility, and asymptotic stability. We demonstrate the effectiveness of our proposed method in simulations on a high-dimensional soft robot with nearly 10,000 states.
Verifiable Reinforcement Learning Systems via Compositionality
Authors: Cyrus Neary, Aryaman Singh Samyal, Christos Verginis, Murat Cubuktepe, Ufuk Topcu
Date: 2023-09-09 00:00:00
Tasks: reinforcement-learning, Reinforcement Learning, Reinforcement Learning (RL)

We propose a framework for verifiable and compositional reinforcement learning (RL) in which a collection of RL subsystems, each of which learns to accomplish a separate subtask, are composed to achieve an overall task. The framework consists of a high-level model, represented as a parametric Markov decision process, which is used to plan and analyze compositions of subsystems, and of the collection of low-level subsystems themselves. The subsystems are implemented as deep RL agents operating under partial observability. By defining interfaces between the subsystems, the framework enables automatic decompositions of task specifications, e.g., reach a target set of states with a probability of at least 0.95, into individual subtask specifications, i.e. achieve the subsystem's exit conditions with at least some minimum probability, given that its entry conditions are met. This in turn allows for the independent training and testing of the subsystems. We present theoretical results guaranteeing that if each subsystem learns a policy satisfying its subtask specification, then their composition is guaranteed to satisfy the overall task specification. Conversely, if the subtask specifications cannot all be satisfied by the learned policies, we present a method, formulated as the problem of finding an optimal set of parameters in the high-level model, to automatically update the subtask specifications to account for the observed shortcomings. The result is an iterative procedure for defining subtask specifications, and for training the subsystems to meet them. Experimental results demonstrate the presented framework's novel capabilities in environments with both full and partial observability, discrete and continuous state and action spaces, as well as deterministic and stochastic dynamics.
Unsupervised Machine Learning Techniques for Exploring Tropical Coamoeba, Brane Tilings and Seiberg Duality
Authors: Rak-Kyeong Seong
Date: 2023-09-11 00:00:00

We introduce unsupervised machine learning techniques in order to identify toric phases of 4d N=1 supersymmetric gauge theories corresponding to the same toric Calabi-Yau 3-fold. These 4d N=1 supersymmetric gauge theories are worldvolume theories of a D3-brane probing a toric Calabi-Yau 3-fold and are realized in terms of a Type IIB brane configuration known as a brane tiling. It corresponds to the skeleton graph of the coamoeba projection of the mirror curve associated to the toric Calabi-Yau 3-fold. When we vary the complex structure moduli of the mirror Calabi-Yau 3-fold, the coamoeba and the corresponding brane tilings change their shape, giving rise to different toric phases related by Seiberg duality. We illustrate that by employing techniques such as principal component analysis (PCA) and t-distributed stochastic neighbor embedding (t-SNE), we can project the space of coamoeba labelled by complex structure moduli down to a lower dimensional phase space with phase boundaries corresponding to Seiberg duality. In this work, we illustrate this technique by obtaining a 2-dimensional phase diagram for brane tilings corresponding to the cone over the zeroth Hirzebruch surface F0.
A novel algebraic approach to time-reversible evolutionary models
Authors: Marta Casanellas, Roser Homs Pons, Angélica Torres
Date: 2023-09-05 00:00:00
Tasks: Model Selection

In the last years, algebraic tools have been proven useful in phylogenetic reconstruction and model selection through the study of phylogenetic invariants. However, up to now, the models studied from an algebraic viewpoint are either too general or too restrictive (as group-based models with a uniform stationary distribution) to be used in practice. In this paper we provide a new framework to study time-reversible models, which are the most widely used by biologists. In our approach we consider algebraic time-reversible models on phylogenetic trees (as defined by Allman and Rhodes) and introduce a new inner product to make all transition matrices of the process diagonalizable through the same orthogonal eigenbasis. This framework generalizes the Fourier transform widely used to work with group-based models and recovers some of the well known results. As illustration, we combine our technique with algebraic geometry tools to provide relevant phylogenetic invariants for trees evolving under the Tamura-Nei model of nucleotide substitution.
Inferring Long-term Dynamics of Ecological Communities Using Combinatorics
Authors: William S. Cuello, Marcio Gameiro, Juan A. Bonachela, Konstantin Mischaikow
Date: 2023-09-01 00:00:00

In an increasingly changing world, predicting the fate of species across the globe has become a major concern. Understanding how the population dynamics of various species and communities will unfold requires predictive tools that experimental data alone can not capture. Here, we introduce our combinatorial framework, Widespread Ecological Networks and their Dynamical Signatures (WENDyS) which, using data on the relative strengths of interactions and growth rates within a community of species predicts all possible long-term outcomes of the community. To this end, WENDyS partitions the multidimensional parameter space (formed by the strengths of interactions and growth rates) into a finite number of regions, each corresponding to a unique set of coarse population dynamics. Thus, WENDyS ultimately creates a library of all possible outcomes for the community. On the one hand, our framework avoids the typical ``parameter sweeps'' that have become ubiquitous across other forms of mathematical modeling, which can be computationally expensive for ecologically realistic models and examples. On the other hand, WENDyS opens the opportunity for interdisciplinary teams to use standard experimental data (i.e., strengths of interactions and growth rates) to filter down the possible end states of a community. To demonstrate the latter, here we present a case study from the Indonesian Coral Reef. We analyze how different interactions between anemone and anemonefish species lead to alternative stable states for the coral reef community, and how competition can increase the chance of exclusion for one or more species. WENDyS, thus, can be used to anticipate ecological outcomes and test the effectiveness of management (e.g., conservation) strategies.
Interpolation, Approximation and Controllability of Deep Neural Networks
Authors: Jingpu Cheng, Qianxiao Li, Ting Lin, Zuowei Shen
Date: 2023-09-12 00:00:00

We investigate the expressive power of deep residual neural networks idealized as continuous dynamical systems through control theory. Specifically, we consider two properties that arise from supervised learning, namely universal interpolation - the ability to match arbitrary input and target training samples - and the closely related notion of universal approximation - the ability to approximate input-target functional relationships via flow maps. Under the assumption of affine invariance of the control family, we give a characterisation of universal interpolation, showing that it holds for essentially any architecture with non-linearity. Furthermore, we elucidate the relationship between universal interpolation and universal approximation in the context of general control systems, showing that the two properties cannot be deduced from each other. At the same time, we identify conditions on the control family and the target function that ensures the equivalence of the two notions.
A General Description of Criticality in Neural Network Models
Authors: Longbin Zeng, Fengjian Feng, Wenlian Lu
Date: 2023-08-25 00:00:00

Recent experimental observations have supported the hypothesis that the cerebral cortex operates in a dynamical regime near criticality, where the neuronal network exhibits a mixture of ordered and disordered patterns. However, A comprehensive study of how criticality emerges and how to reproduce it is still lacking. In this study, we investigate coupled networks with conductance-based neurons and illustrate the co-existence of different spiking patterns, including asynchronous irregular (AI) firing and synchronous regular (SR) state, along with a scale-invariant neuronal avalanche phenomenon (criticality). We show that fast-acting synaptic coupling can evoke neuronal avalanches in the mean-dominated regime but has little effect in the fluctuation-dominated regime. In a narrow region of parameter space, the network exhibits avalanche dynamics with power-law avalanche size and duration distributions. We conclude that three stages which may be responsible for reproducing the synchronized bursting: mean-dominated subthreshold dynamics, fast-initiating a spike event, and time-delayed inhibitory cancellation. Remarkably, we illustrate the mechanisms underlying critical avalanches in the presence of noise, which can be explained as a stochastic crossing state around the Hopf bifurcation under the mean-dominated regime. Moreover, we apply the ensemble Kalman filter to determine and track effective connections for the neuronal network. The method is validated on noisy synthetic BOLD signals and could exactly reproduce the corresponding critical network activity. Our results provide a special perspective to understand and model the criticality, which can be useful for large-scale modeling and computation of brain dynamics.
Generalized Rainbow Differential Privacy
Authors: Yuzhou Gu, Ziqi Zhou, Onur Günlü, Rafael G. L. D'Oliveira, Parastoo Sadeghi, Muriel Médard, Rafael F. Schaefer
Date: 2023-09-11 00:00:00
Tasks: valid

We study a new framework for designing differentially private (DP) mechanisms via randomized graph colorings, called rainbow differential privacy. In this framework, datasets are nodes in a graph, and two neighboring datasets are connected by an edge. Each dataset in the graph has a preferential ordering for the possible outputs of the mechanism, and these orderings are called rainbows. Different rainbows partition the graph of connected datasets into different regions. We show that if a DP mechanism at the boundary of such regions is fixed and it behaves identically for all same-rainbow boundary datasets, then a unique optimal $(\epsilon,\delta)$-DP mechanism exists (as long as the boundary condition is valid) and can be expressed in closed-form. Our proof technique is based on an interesting relationship between dominance ordering and DP, which applies to any finite number of colors and for $(\epsilon,\delta)$-DP, improving upon previous results that only apply to at most three colors and for $\epsilon$-DP. We justify the homogeneous boundary condition assumption by giving an example with non-homogeneous boundary condition, for which there exists no optimal DP mechanism.
Chebyshev Particles
Authors: Xiongming Dai, Gerald Baumgartner
Date: 2023-09-10 00:00:00

Markov chain Monte Carlo (MCMC) provides a feasible method for inferring Hidden Markov models, however, it is often computationally prohibitive, especially constrained by the curse of dimensionality, as the Monte Carlo sampler traverses randomly taking small steps within uncertain regions in the parameter space. We are the first to consider the posterior distribution of the objective as a mapping of samples in an infinite-dimensional Euclidean space where deterministic submanifolds are embedded and propose a new criterion by maximizing the weighted Riesz polarization quantity, to discretize rectifiable submanifolds via pairwise interaction. We study the characteristics of Chebyshev particles and embed them into sequential MCMC, a novel sampler with a high acceptance ratio that proposes only a few evaluations. We have achieved high performance from the experiments for parameter inference in a linear Gaussian state-space model with synthetic data and a non-linear stochastic volatility model with real-world data.
Improved Monte Carlo tree search formulation with multiple root nodes for discrete sizing optimization of truss structures
Authors: Fu-Yao Ko, Katsuyuki Suzuki, Kazuo Yonekura
Date: 2023-09-12 00:00:00
Tasks: Reinforcement Learning (RL)

This paper proposes a novel reinforcement learning (RL) algorithm using improved Monte Carlo tree search (IMCTS) formulation for discrete optimum design of truss structures. IMCTS with multiple root nodes includes update process, the best reward, accelerating technique, and terminal condition. Update process means that once a final solution is found, it is used as the initial solution for next search tree. The best reward is used in the backpropagation step. Accelerating technique is introduced by decreasing the width of search tree and reducing maximum number of iterations. The agent is trained to minimize the total structural weight under various constraints until the terminal condition is satisfied. Then, optimal solution is the minimum value of all solutions found by search trees. These numerical examples show that the agent can find optimal solution with low computational cost, stably produces an optimal design, and is suitable for multi-objective structural optimization and large-scale structures.
Tumoral Angiogenic Optimizer: A new bio-inspired based metaheuristic
Authors: Hernández Rodríguez, Matías Ezequiel
Date: 2023-09-12 00:00:00
Tasks: Cantilever Beam

In this article, we propose a new metaheuristic inspired by the morphogenetic cellular movements of endothelial cells (ECs) that occur during the tumor angiogenesis process. This algorithm starts with a random initial population. In each iteration, the best candidate selected as the tumor, while the other individuals in the population are treated as ECs migrating toward the tumor's direction following a coordinated dynamics through a spatial relationship between tip and follower ECs. This algorithm has an advantage compared to other similar optimization metaheuristics: the model parameters are already configured according to the tumor angiogenesis phenomenon modeling, preventing researchers from initializing them with arbitrary values. Subsequently, the algorithm is compared against well-known benchmark functions, and the results are validated through a comparative study with Particle Swarm Optimization (PSO). The results demonstrate that the algorithm is capable of providing highly competitive outcomes. Furthermore, the proposed algorithm is applied to real-world problems (cantilever beam design, pressure vessel design, tension/compression spring and sustainable explotation renewable resource). The results showed that the proposed algorithm worked effectively in solving constrained optimization problems. The results obtained were compared with several known algorithms.
ELRA: Exponential learning rate adaption gradient descent optimization method
Authors: Alexander Kleinsorge, Stefan Kupper, Alexander Fauck, Felix Rothe
Date: 2023-09-12 00:00:00

We present a novel, fast (exponential rate adaption), ab initio (hyper-parameter-free) gradient based optimizer algorithm. The main idea of the method is to adapt the learning rate $\alpha$ by situational awareness, mainly striving for orthogonal neighboring gradients. The method has a high success and fast convergence rate and does not rely on hand-tuned parameters giving it greater universality. It can be applied to problems of any dimensions n and scales only linearly (of order O(n)) with the dimension of the problem. It optimizes convex and non-convex continuous landscapes providing some kind of gradient. In contrast to the Ada-family (AdaGrad, AdaMax, AdaDelta, Adam, etc.) the method is rotation invariant: optimization path and performance are independent of coordinate choices. The impressive performance is demonstrated by extensive experiments on the MNIST benchmark data-set against state-of-the-art optimizers. We name this new class of optimizers after its core idea Exponential Learning Rate Adaption - ELRA. We present it in two variants c2min and p2min with slightly different control. The authors strongly believe that ELRA will open a completely new research direction for gradient descent optimize.
Geometry of vectorial martingale optimal transport and robust option pricing
Authors: Joshua Zoen-Git Hiew, Tongseok Lim, Brendan Pass, Marcelo Cruz de Souza
Date: 2023-09-10 00:00:00

This paper addresses robust finance, which is concerned with the development of models and approaches that account for market uncertainties. Specifically, we investigate the Vectorial Martingale Optimal Transport (VMOT) problem, the geometry of its solutions, and its application with robust option pricing problems in finance. To this end, we consider two-period market models and show that when the spatial dimension $d$ (the number of underlying assets) is 2, the extremal model for the cap option with a sub- or super-modular payout reduces to a single factor model in the first period, but not in general when $d > 2$. The result demonstrates a subtle relationship between spatial dimension, cost function supermodularity, and their effect on the geometry of solutions to the VMOT problem. We investigate applications of the model to financial problems and demonstrate how the dimensional reduction caused by monotonicity can be used to improve existing computational methods.