Model Reduction and Neural Networks

Derniers papiers

• A Physics-Informed Neural Network with a Modified Lorentzian Activation for Nonlocal Gradient-Flow Equations in Dynamic Density Functional Theory

  Dimitrios Gourzoulidis, Soumaya Elkantassi, Serafim Kalliadasis · 20 juillet 2026

  We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT). Such equations are challenging for standard PINN methods because they involve nonlinearities, nonlocal interaction terms, and an underlying g…

• Trainable Spline Representations for Physics-Informed Learning

  Giovanni Canali, Nicola Demo, Gianluigi Rozza · 20 juillet 2026

  This work introduces Physics-Informed Splines (PI-Splines), a structured spline-based architecture for physics-informed learning. Instead of representing the solution of a differential equation with a neural network, PI-Splines directly parametrize the unknown field through a tensor-product B-spline…

• Discovering Generalizable Governing Equations for Graph Dynamical Systems with Interpretable Neural Networks

  Riccardo Cappi, Paolo Frazzetto, Nicol\`o Navarin, Alessandro Sperduti · 20 juillet 2026

  The discovery of symbolic governing equations is a central goal in science; yet, it remains challenging particularly for graph dynamical systems, where the network topology further shapes the system behavior. While artificial intelligence offers powerful tools for modeling these dynamics, the field …

• Physics-enhanced reinforcement learning for real-time optimal control of dynamical systems

  Matteo Tomasetto, Nicol\`o Botteghi, Gabriele Bruni, Andrea Manzoni · 20 juillet 2026

  Reinforcement learning (RL) has recently emerged as a promising feedback control strategy for nonlinear and complex dynamical systems. However, RL algorithms are sample inefficient and require a large number of interaction with the environment to synthesize optimal control strategies. Consequently, …

• Evolutionary Algorithm-Guided LLMs for Physics-Informed Neural Network Design

  Xu Yang, Mingyang Yu, Jing Xu, Keqian Li · 20 juillet 2026

  Physics-informed neural networks (PINNs) are unusually sensitive to interacting choices of architecture, activation, loss weighting, collocation, optimization, and constraint enforcement. Large language models (LLMs) can propose these choices, but independent recommendations do not accumulate experi…

• A Statistical Formulation Gap for Nonlinear Multiscale Physics-Informed Learning

  Ronald Katende · 20 juillet 2026

  We prove a finite-sample formulation gap for physics-informed learning of nonlinear multiscale elliptic equations. For a uniformly monotone divergence-form class with coefficients oscillating at scale $\epsilon$, we derive a finite-width, finite-sample, and finite-iteration error bound for a boundar…

• Optimal Self-Distillation for Rectified Flow via Linear Probing

  Saptarshi Roy, Debepsita Mukherjee, Pratik Patil · 17 juillet 2026

  Modern generative models are increasingly trained using model-generated signals, creating both opportunities for self-improvement and risks of collapse. We study optimal self-distillation (SD) for rectified flow (RF): given a suboptimal teacher velocity field, can a student trained on a mixture of t…

• Adaptive Runge-Kutta Step Control Buys Training Loss, Not Generalization: An Honest Compute-Matched Study of RK-Adam Optimizers

  Akhilesh Gogikar · 17 juillet 2026

  Interpreting optimizers as gradient-flow discretizations has motivated applying higher-order Runge-Kutta (RK) integrators to neural networks. We build a representative Adam variant (Bogacki-Shampine 3(2) RK pair, FSAL reuse, local-error step control) and evaluate it under a strict compute-matched pr…

• LIGO-PINN: Learned Initialization via Gated Optimization to Alleviate Convergence Failures in Physics Informed Neural Networks

  Nilay Anurag, Shital Adhikari, Taniya Kapoor, Nikhil Muralidhar · 17 juillet 2026

  Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE). However, PINNs have been shown to perform poorly, sometimes even converging to trivial solutions, in challenging PDE domains, or when generalizing to unseen…

• RTS Smoother-Guided Learning of Physics-Based Neural Differential Models

  Ahmet Demirkaya, Georgios Stratis, Tales Imbiriba, Zachary D. Danziger, Deniz Erdogmus · 17 juillet 2026

  Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured. We propose a hybrid neural--physics framewor…

• A Minimal Interpretable Architecture for Zero-Shot Reconstruction of Dynamical Systems

  Christoph J\"urgen Hemmer, Florian Plaswig, Daniel Durstewitz · 17 juillet 2026

  Recent foundation models (FMs) for zero-shot reconstruction of dynamical systems (DS) achieve strong out-of-domain generalization but provide little insight into the mechanisms that underlie their forecasts. Such an understanding could help to strip down overladen FM architectures to their bare esse…

• An Introduction to Sparse Identification of Nonlinear Dynamics for Engineering Applications

  Yao Cheng Li, Ana Larra\~naga, Steven L. Brunton, Urban Fasel · 17 juillet 2026

  Many engineering problems involve phenomena whose governing equations are poorly characterized or only partially known. Surrogate modeling techniques such as neural networks can capture the behavior of these systems, but they typically demand large training datasets that are difficult to obtain in e…

• NeuralChaos: Optimal Adapted Approximation of Square Integrable Predictable Processes

  Anastasis Kratsios, Giulia Livieri, Philipp Schmocker · 17 juillet 2026

  We address fundamental challenges in representing and computing $\mathbb{R}^{d}$-valued predictable square-integrable processes over $[0,T]$, collected in the space $\mathcal{H}^2_T(\mathbb{R}^{d})$. These processes are central to continuous-time stochastic control, reinforcement learning, and mathe…

• Subgrid-Scale Parameterization in Burgers' Equation Using Structure-Preserving Neural Networks and Entropy Variables

  Aijaz Nazir, Ilya Timofeyev · 17 juillet 2026

  We present a machine learning approach for developing subgrid-scale (SGS) parametrizations in coarse simulations of partial differential equations. We utilize structure-preserving neural networks and entropy variables to learn subgrid fluxes in coarse simulations of the Burgers' equation. In particu…

• Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Data

  Tatthapong Srikitrungruang, Jaesung Lee · 17 juillet 2026

  Estimating spatially heterogeneous elastic properties from low-resolution displacement measurements is a severely ill-posed inverse elasticity problem because low resolution obscures spatial details needed to distinguish heterogeneous property variations, and small measurement perturbations or fitti…

• Sharp Stability Threshold and Certification for Designing Stable Residual Architectures

  Hyemin Gu, Michael Tyrrell, Tuhin Sahai, Markos A. Katsoulakis · 17 juillet 2026

  We propose \emph{the sublinear-growth principle} for deep residual architectures -- a sharp stability threshold on the input-magnitude exponent of every residual block's velocity field: $$\|v(x, t)\| \leq c\,\|x\|^q + b, \qquad q \in [0, 1].$$ The threshold $q = 1$ is established via two independent…

• Operator-Informed Gaussian Processes for Complex Helmholtz Wavefields: From Synthetic Benchmarks to In Vivo Brain Elastography

  Boyuan Deng, Kshitiz Upadhyay, Michael Shields · 17 juillet 2026

  The Helmholtz equation governs time-harmonic wave propagation, and in dissipative media a complex modulus renders its squared wavenumber $\kappa^2$ complex. Inferring such fields from sparse, noisy data calls for solvers that also quantify their own uncertainty. Physics-informed Gaussian-process (GP…

• Automatic Ordinary Differential Equations Discovery For Biological Systems Using Large Language Model Powered Agentic System

  David Krongauz, Arad Zulti, Eran Segal, Teddy Lazebnik · 16 juillet 2026

  Automatic scientific discovery has long been a goal of computational scholars - a machine that can discover nature's secrets on its own, moving computational systems beyond data-fitting tools toward the generation and refinement of mechanistic models of the universe. Recent advances in symbolic regr…

• Discrete Diffusion Models: A Unified Framework from Tokenization to Generation

  Ye Yuan, Weien Li, Rui Song, Zeyu Li, Haochen Liu, Xiangyu Kong, Zixuan Dong, Linfeng Du, Zipeng Sun, Weixu Zhang, Jiaxin Huang, Changjiang Han, Yonghan Yang, Zichen Zhao, Xiuyuan Hu, Haolun Wu, Yankai Chen, Fengran Mo, Jikun Kang, Bowei He, Philip S. Yu, Xue Liu · 16 juillet 2026

  Discrete denoising diffusion models (DDMs) have recently emerged as a compelling alternative to autoregressive (AR) modeling for discrete data, offering parallel generation and iterative global refinement capabilities. Unlike continuous diffusion, where the state space is fixed, DDMs are fundamental…

• Spectral-Informed Neural Networks Outperform Spectral Methods in High-dimensional PDEs

  Tianchi Yu, Ivan Oseledets · 16 juillet 2026

  For low-dimensional problems ($d\leq3$), spectral methods can achieve exceptionally high accuracy. For middle-dimensional problems ($4 \leq d \lesssim 10$), spectral methods remain feasible through specific techniques such as sparse grids or hyperbolic cross. However, for high-dimensional problems (…

• Automatic Differentiation from Scratch: How PyTorch Computes Gradients in Physics-Informed Neural Networks

  Abdeladhim Tahimi · 16 juillet 2026

  This paper traces, with explicit numerical values, how PyTorch's automatic differentiation (AD) engine computes gradients for Physics-Informed Neural Network (PINN) training -- a setting that requires two levels of differentiation: computing the physics derivative $\hat{y}'(t)=d\hat{y}/dt$ through t…

• Gradient-free learning of a closed-loop wall controller for turbulent drag reduction

  Giorgio Maria Cavallazzi, Miguel P\'erez Cuadrado, Alfredo Pinelli · 15 juillet 2026

  Closed-loop wall control learnt by multi-agent reinforcement learning can lower skin-friction drag in turbulent channels, but these gradient-based policies are trained on small periodic boxes and exhibit reduced performance when carried over to a larger domain. We recently showed that such policies …

• Learning Forced Multibody Dynamics on Lie Groups

  Martine Dyring Hansen, Marta Ghirardelli, Elena Celledoni, David Martin de Diego, Brynjulf Owren · 15 juillet 2026

  We propose an architecture for learning the dynamics of mechanical systems based on discrete forced Euler-Lagrange equations on Lie groups using only position data. By formulating the dynamics directly on manifold-valued configuration spaces, the method naturally respects the geometric structure of …

• A Shortcut to Statistically Steady-State Turbulence with Flow Matching

  Gianluca Galletti, Gerald Gutenbrunner, William Hornsby, Lorenzo Zanisi, Naomi Carey, Stanislas Pamela, Johannes Brandstetter, Fabian Paischer · 15 juillet 2026

  Many nonlinear physical systems exhibit an initial transient phase in which perturbations grow before nonlinear interactions lead to a statistically steady state. While this saturated regime is of primary interest, direct numerical simulations must resolve the full transient dynamics before reaching…

• Learning to Discretize: Diffusion-Based Adaptive Mesh with Spectral Guidance

  Zixuan Shen (Central South University), Bingchuan Wang (Central South University), Zhi Wang (Nanjing University), Yong Wang (Central South University) · 15 juillet 2026

  Most neural partial differential equation (PDE) surrogates learn how fields evolve after a grid has already been chosen. However, before any operator is applied, the grid has already determined how modeling capacity is allocated across space, resolution, and spectral bandwidth. We argue that this hi…