Model Reduction and Neural Networks

Derniers papiers

• Symmetry-Aware Steering of Equivariant Diffusion Policies: Benefits and Limits

  Minwoo Park, Junwoo Chang, Jongeun Choi, Roberto Horowitz · 15 décembre 2025

  Equivariant diffusion policies (EDPs) combine the generative expressivity of diffusion models with the strong generalization and sample efficiency afforded by geometric symmetries. While steering these policies with reinforcement learning (RL) offers a promising mechanism for fine-tuning beyond demo…

• Bhargava Cube--Inspired Quadratic Regularization for Structured Neural Embeddings

  S Sairam, Prateek P Kulkarni · 15 décembre 2025

  We present a novel approach to neural representation learning that incorporates algebraic constraints inspired by Bhargava cubes from number theory. Traditional deep learning methods learn representations in unstructured latent spaces lacking interpretability and mathematical consistency. Our framew…

• Data-Driven Model Reduction using WeldNet: Windowed Encoders for Learning Dynamics

  Biraj Dahal, Jiahui Cheng, Hao Liu, Rongjie Lai, Wenjing Liao · 15 décembre 2025

  Many problems in science and engineering involve time-dependent, high dimensional datasets arising from complex physical processes, which are costly to simulate. In this work, we propose WeldNet: Windowed Encoders for Learning Dynamics, a data-driven nonlinear model reduction framework to build a lo…

• The Vekua Layer: Exact Physical Priors for Implicit Neural Representations via Generalized Analytic Functions

  Vladimer Khasia · 15 décembre 2025

  Implicit Neural Representations (INRs) have emerged as a powerful paradigm for parameterizing physical fields, yet they often suffer from spectral bias and the computational expense of non-convex optimization. We introduce the Vekua Layer (VL), a differentiable spectral method grounded in the classi…

• On the failure of ReLU activation for physics-informed machine learning

  Conor Rowan · 15 décembre 2025

  Physics-informed machine learning uses governing ordinary and/or partial differential equations to train neural networks to represent the solution field. Like any machine learning problem, the choice of activation function influences the characteristics and performance of the solution obtained from …

• Misspecification-robust amortised simulation-based inference using variational methods

  Matthew O'Callaghan, Kaisey S. Mandel, Gerry Gilmore · 15 décembre 2025

  Recent advances in neural density estimation have enabled powerful simulation-based inference (SBI) methods that can flexibly approximate Bayesian inference for intractable stochastic models. Although these methods have demonstrated reliable posterior estimation when the simulator accurately represe…

• Geometry-Informed Neural Operator Transformer

  Qibang Liu, Weiheng Zhong, Hadi Meidani, Diab Abueidda, Seid Koric, Philippe Geubelle · 15 décembre 2025

  Machine-learning-based surrogate models offer significant computational efficiency and faster simulations compared to traditional numerical methods, especially for problems requiring repeated evaluations of partial differential equations. This work introduces the Geometry-Informed Neural Operator Tr…

• Stable spectral neural operator for learning stiff PDE systems from limited data

  Rui Zhang, Han Wan, Yang Liu, Hao Sun · 15 décembre 2025

  Accurate modeling of spatiotemporal dynamics is crucial to understanding complex phenomena across science and engineering. However, this task faces a fundamental challenge when the governing equations are unknown and observational data are sparse. System stiffness, the coupling of multiple time-scal…

• Generative Parametric Design (GPD): A framework for real-time geometry generation and on-the-fly multiparametric approximation

  Mohammed El Fallaki Idrissi, Jad Mounayer, Sebastian Rodriguez, Fodil Meraghni, Francisco Chinesta · 15 décembre 2025

  This paper presents a novel paradigm in simulation-based engineering sciences by introducing a new framework called Generative Parametric Design (GPD). The GPD framework enables the generation of new designs along with their corresponding parametric solutions given as a reduced basis. To achieve thi…

• The Adaptive Vekua Cascade: A Differentiable Spectral-Analytic Solver for Physics-Informed Representation

  Vladimer Khasia · 15 décembre 2025

  Coordinate-based neural networks have emerged as a powerful tool for representing continuous physical fields, yet they face two fundamental pathologies: spectral bias, which hinders the learning of high-frequency dynamics, and the curse of dimensionality, which causes parameter explosion in discrete…

• NeuralOGCM: Differentiable Ocean Modeling with Learnable Physics

  Hao Wu, Yuan Gao, Fan Xu, Fan Zhang, Guangliang Liu, Yuxuan Liang, Xiaomeng Huang · 15 décembre 2025

  High-precision scientific simulation faces a long-standing trade-off between computational efficiency and physical fidelity. To address this challenge, we propose NeuralOGCM, an ocean modeling framework that fuses differentiable programming with deep learning. At the core of NeuralOGCM is a fully di…

• Parametric Numerical Integration with (Differential) Machine Learning

  \'Alvaro Leitao, Jonatan R\'afales · 15 décembre 2025

  In this work, we introduce a machine/deep learning methodology to solve parametric integrals. Besides classical machine learning approaches, we consider a differential learning framework that incorporates derivative information during training, emphasizing its advantageous properties. Our study cove…

• Generalized Spherical Neural Operators: Green's Function Formulation

  Hao Tang, Hao Chen, Chao Li · 12 décembre 2025

  Neural operators offer powerful approaches for solving parametric partial differential equations, but extending them to spherical domains remains challenging due to the need to preserve intrinsic geometry while avoiding distortions that break rotational consistency. Existing spherical operators rely…

• Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels

  Quanjun Lang, Jianfeng Lu · 12 décembre 2025

  We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory discrepancies decay at a rate determined by the decay of the memory…

• A Kernel-based Resource-efficient Neural Surrogate for Multi-fidelity Prediction of Aerodynamic Field

  Apurba Sarker, Reza T. Batley, Darshan Sarojini, Sourav Saha · 12 décembre 2025

  Surrogate models provide fast alternatives to costly aerodynamic simulations and are extremely useful in design and optimization applications. This study proposes the use of a recent kernel-based neural surrogate, KHRONOS. In this work, we blend sparse high-fidelity (HF) data with low-fidelity (LF) …

• Physics-informed Polynomial Chaos Expansion with Enhanced Constrained Optimization Solver and D-optimal Sampling

  Qitian Lu, Himanshu Sharma, Michael D. Shields, Luk\'a\v{s} Nov\'ak · 12 décembre 2025

  Physics-informed polynomial chaos expansions (PC$^2$) provide an efficient physically constrained surrogate modeling framework by embedding governing equations and other physical constraints into the standard data-driven polynomial chaos expansions (PCE) and solving via the Karush-Kuhn-Tucker (KKT) …

• Lazy Diffusion: Mitigating spectral collapse in generative diffusion-based stable autoregressive emulation of turbulent flows

  Anish Sambamurthy, Ashesh Chattopadhyay · 11 décembre 2025

  Turbulent flows posses broadband, power-law spectra in which multiscale interactions couple high-wavenumber fluctuations to large-scale dynamics. Although diffusion-based generative models offer a principled probabilistic forecasting framework, we show that standard DDPMs induce a fundamental \emph{…

• Banach neural operator for Navier-Stokes equations

  Bo Zhang · 11 décembre 2025

  Classical neural networks are known for their ability to approximate mappings between finite-dimensional spaces, but they fall short in capturing complex operator dynamics across infinite-dimensional function spaces. Neural operators, in contrast, have emerged as powerful tools in scientific machine…

• Tensor-Compressed and Fully-Quantized Training of Neural PDE Solvers

  Jinming Lu, Jiayi Tian, Yequan Zhao, Hai Li, Zheng Zhang · 11 décembre 2025

  Physics-Informed Neural Networks (PINNs) have emerged as a promising paradigm for solving partial differential equations (PDEs) by embedding physical laws into neural network training objectives. However, their deployment on resource-constrained platforms is hindered by substantial computational and…

• SynthPix: A lightspeed PIV images generator

  Antonio Terpin, Alan Bonomi, Francesco Banelli, Raffaello D'Andrea · 11 décembre 2025

  We describe SynthPix, a synthetic image generator for Particle Image Velocimetry (PIV) with a focus on performance and parallelism on accelerators, implemented in JAX. SynthPix supports the same configuration parameters as existing tools but achieves a throughput several orders of magnitude higher i…

• Spectral Embedding via Chebyshev Bases for Robust DeepONet Approximation

  Muhammad Abid, Omer San · 11 décembre 2025

  Deep Operator Networks (DeepONets) have become a central tool in data-driven operator learning, providing flexible surrogates for nonlinear mappings arising in partial differential equations (PDEs). However, the standard trunk design based on fully connected layers acting on raw spatial or spatiotem…

• CarBench: A Comprehensive Benchmark for Neural Surrogates on High-Fidelity 3D Car Aerodynamics

  Mohamed Elrefaie, Dule Shu, Matt Klenk, Faez Ahmed · 10 décembre 2025

  Benchmarking has been the cornerstone of progress in computer vision, natural language processing, and the broader deep learning domain, driving algorithmic innovation through standardized datasets and reproducible evaluation protocols. The growing availability of large-scale Computational Fluid Dyn…

• Worst-case generation via minimax optimization in Wasserstein space

  Xiuyuan Cheng, Yao Xie, Linglingzhi Zhu, Yunqin Zhu · 10 décembre 2025

  Worst-case generation plays a critical role in evaluating robustness and stress-testing systems under distribution shifts, in applications ranging from machine learning models to power grids and medical prediction systems. We develop a generative modeling framework for worst-case generation for a pr…

• Wavelet-Accelerated Physics-Informed Quantum Neural Network for Multiscale Partial Differential Equations

  Deepak Gupta, Himanshu Pandey, Ratikanta Behera · 10 décembre 2025

  This work proposes a wavelet-based physics-informed quantum neural network framework to efficiently address multiscale partial differential equations that involve sharp gradients, stiffness, rapid local variations, and highly oscillatory behavior. Traditional physics-informed neural networks (PINNs)…

• Fredholm Neural Networks for forward and inverse problems in elliptic PDEs

  Kyriakos Georgiou, Constantinos Siettos, Athanasios N. Yannacopoulos · 9 décembre 2025

  Building on our previous work introducing Fredholm Neural Networks (Fredholm NNs/ FNNs) for solving integral equations, we extend the framework to tackle forward and inverse problems for linear and semi-linear elliptic partial differential equations. The proposed scheme consists of a deep neural net…