Model Reduction and Neural Networks

Derniers papiers

• How does training shape the Riemannian geometry of neural network representations?

  Jacob A. Zavatone-Veth, Sheng Yang, Julian A. Rubinfien, Cengiz Pehlevan · 6 novembre 2025

  In machine learning, there is a long history of trying to build neural networks that can learn from fewer example data by baking in strong geometric priors. However, it is not always clear a priori what geometric constraints are appropriate for a given task. Here, we explore the possibility that one…

• A unified physics-informed generative operator framework for general inverse problems

  Gang Bao, Yaohua Zang · 6 novembre 2025

  Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or discontinuous. Existing deep learning approaches either require e…

• Compliance Minimization via Physics-Informed Gaussian Processes

  Xiangyu Sun, Amin Yousefpour, Shirin Hosseinmardi, Ramin Bostanabad · 6 novembre 2025

  Machine learning (ML) techniques have recently gained significant attention for solving compliance minimization (CM) problems. However, these methods typically provide poor feature boundaries, are very expensive, and lack a systematic mechanism to control the design complexity. Herein, we address th…

• Finding geodesics with the Deep Ritz method

  Conor Rowan · 6 novembre 2025

  Geodesic problems involve computing trajectories between prescribed initial and final states to minimize a user-defined measure of distance, cost, or energy. They arise throughout physics and engineering -- for instance, in determining optimal paths through complex environments, modeling light propa…

• Reliable and efficient inverse analysis using physics-informed neural networks with normalized distance functions and adaptive weight tuning

  Shota Deguchi, Mitsuteru Asai · 6 novembre 2025

  Physics-informed neural networks have attracted significant attention in scientific machine learning for their capability to solve forward and inverse problems governed by partial differential equations. However, the accuracy of PINN solutions is often limited by the treatment of boundary conditions…

• Learning Under Laws: A Constraint-Projected Neural PDE Solver that Eliminates Hallucinations

  Mainak Singha · 6 novembre 2025

  Neural networks can approximate solutions to partial differential equations, but they often break the very laws they are meant to model-creating mass from nowhere, drifting shocks, or violating conservation and entropy. We address this by training within the laws of physics rather than beside them. …

• Automatic Discovery of One-Parameter Subgroups of Lie Groups: Compact and Non-Compact Cases of $\mathbf{SO(n)}$ and $\mathbf{SL(n)}$

  Pavan Karjol, Vivek V Kashyap, Rohan Kashyap, Prathosh A P · 6 novembre 2025

  We introduce a novel framework for the automatic discovery of one-parameter subgroups ($H_{\gamma}$) of $SO(3)$ and, more generally, $SO(n)$. One-parameter subgroups of $SO(n)$ are crucial in a wide range of applications, including robotics, quantum mechanics, and molecular structure analysis. Our m…

• Remasking Discrete Diffusion Models with Inference-Time Scaling

  Guanghan Wang, Yair Schiff, Subham Sekhar Sahoo, Volodymyr Kuleshov · 5 novembre 2025

  Part of the success of diffusion models stems from their ability to perform iterative refinement, i.e., repeatedly correcting outputs during generation. However, modern masked discrete diffusion lacks this capability: when a token is generated, it cannot be updated again, even when it introduces an …

• Bulk-boundary decomposition of neural networks

  Donghee Lee, Hye-Sung Lee, Jaeok Yi · 5 novembre 2025

  We present the bulk-boundary decomposition as a new framework for understanding the training dynamics of deep neural networks. Starting from the stochastic gradient descent formulation, we show that the Lagrangian can be reorganized into a data-independent bulk term and a data-dependent boundary ter…

• NOWS: Neural Operator Warm Starts for Accelerating Iterative Solvers

  Mohammad Sadegh Eshaghi, Cosmin Anitescu, Navid Valizadeh, Yizheng Wang, Xiaoying Zhuang, Timon Rabczuk · 5 novembre 2025

  Partial differential equations (PDEs) underpin quantitative descriptions across the physical sciences and engineering, yet high-fidelity simulation remains a major computational bottleneck for many-query, real-time, and design tasks. Data-driven surrogates can be strikingly fast but are often unreli…

• Neural Green's Functions

  Seungwoo Yoo, Kyeongmin Yeo, Jisung Hwang, Minhyuk Sung · 5 novembre 2025

  We introduce Neural Green's Function, a neural solution operator for linear partial differential equations (PDEs) whose differential operators admit eigendecompositions. Inspired by Green's functions, the solution operators of linear PDEs that depend exclusively on the domain geometry, we design Neu…

• In Situ Training of Implicit Neural Compressors for Scientific Simulations via Sketch-Based Regularization

  Cooper Simpson, Stephen Becker, Alireza Doostan · 5 novembre 2025

  Focusing on implicit neural representations, we present a novel in situ training protocol that employs limited memory buffers of full and sketched data samples, where the sketched data are leveraged to prevent catastrophic forgetting. The theoretical motivation for our use of sketching as a regulari…

• Reinforcement learning based data assimilation for unknown state model

  Ziyi Wang, Lijian Jiang · 5 novembre 2025

  Data assimilation (DA) has increasingly emerged as a critical tool for state estimation across a wide range of applications. It is signiffcantly challenging when the governing equations of the underlying dynamics are unknown. To this end, various machine learning approaches have been employed to c…

• Automated Discovery of Conservation Laws via Hybrid Neural ODE-Transformers

  Vivan Doshi · 4 novembre 2025

  The discovery of conservation laws is a cornerstone of scientific progress. However, identifying these invariants from observational data remains a significant challenge. We propose a hybrid framework to automate the discovery of conserved quantities from noisy trajectory data. Our approach integrat…

• Structure-Preserving Physics-Informed Neural Network for the Korteweg--de Vries (KdV) Equation

  Victory Obieke, Emmanuel Oguadimma · 4 novembre 2025

  Physics-Informed Neural Networks (PINNs) offer a flexible framework for solving nonlinear partial differential equations (PDEs), yet conventional implementations often fail to preserve key physical invariants during long-term integration. This paper introduces a \emph{structure-preserving PINN} fram…

• HEATNETs: Explainable Random Feature Neural Networks for High-Dimensional Parabolic PDEs

  Kyriakos Georgiou, Gianluca Fabiani, Constantinos Siettos, Athanasios N. Yannacopoulos · 4 novembre 2025

  We deal with the solution of the forward problem for high-dimensional parabolic PDEs with random feature (projection) neural networks (RFNNs). We first prove that there exists a single-hidden layer neural network with randomized heat-kernels arising from the fundamental solution (Green's functions) …

• Fast PINN Eigensolvers via Biconvex Reformulation

  Akshay Sai Banderwaar, Abhishek Gupta · 4 novembre 2025

  Eigenvalue problems have a distinctive forward-inverse structure and are fundamental to characterizing a system's thermal response, stability, and natural modes. Physics-Informed Neural Networks (PINNs) offer a mesh-free alternative for solving such problems but are often orders of magnitude slower …

• One model to solve them all: 2BSDE families via neural operators

  Takashi Furuya, Anastasis Kratsios, Dylan Possama\"i, Bogdan Raoni\'c · 4 novembre 2025

  We introduce a mild generative variant of the classical neural operator model, which leverages Kolmogorov--Arnold networks to solve infinite families of second-order backward stochastic differential equations ($2$BSDEs) on regular bounded Euclidean domains with random terminal time. Our first main r…

• Regularization Implies balancedness in the deep linear network

  Kathryn Lindsey, Govind Menon · 4 novembre 2025

  We use geometric invariant theory (GIT) to study the deep linear network (DLN). The Kempf-Ness theorem is used to establish that the $L^2$ regularizer is minimized on the balanced manifold. This allows us to decompose the training dynamics into two distinct gradient flows: a regularizing flow on fib…

• Lyapunov Stability Learning with Nonlinear Control via Inductive Biases

  Yupu Lu, Shijie Lin, Hao Xu, Zeqing Zhang, Jia Pan · 4 novembre 2025

  Finding a control Lyapunov function (CLF) in a dynamical system with a controller is an effective way to guarantee stability, which is a crucial issue in safety-concerned applications. Recently, deep learning models representing CLFs have been applied into a learner-verifier framework to identify sa…

• Dynamic Reconstruction of Ultrasound-Derived Flow Fields With Physics-Informed Neural Fields

  Viraj Patel, Lisa Kreusser, Katharine Fraser · 4 novembre 2025

  Blood flow is sensitive to disease and provides insight into cardiac function, making flow field analysis valuable for diagnosis. However, while safer than radiation-based imaging and more suitable for patients with medical implants, ultrasound suffers from attenuation with depth, limiting the quali…

• Sensitivity Analysis for Climate Science with Generative Flow Models

  Alex Dobra, Jakiw Pidstrigach, Tim Reichelt, Paolo Fraccaro, Johannes Jakubik, Anne Jones, Christian Schroeder de Witt, Philip Stier, Philip Torr · 4 novembre 2025

  Sensitivity analysis is a cornerstone of climate science, essential for understanding phenomena ranging from storm intensity to long-term climate feedbacks. However, computing these sensitivities using traditional physical models is often prohibitively expensive in terms of both computation and deve…

• Filtered Neural Galerkin model reduction schemes for efficient propagation of initial condition uncertainties in digital twins

  Zhiyang Ning, Benjamin Peherstorfer · 4 novembre 2025

  Uncertainty quantification in digital twins is critical to enable reliable and credible predictions beyond available data. A key challenge is that ensemble-based approaches can become prohibitively expensive when embedded in control and data assimilation loops in digital twins, even when reduced mod…

• Real-Time Learning of Predictive Dynamic Obstacle Models for Robotic Motion Planning

  Stella Kombo, Masih Haseli, Skylar Wei, Joel W. Burdick · 4 novembre 2025

  Autonomous systems often must predict the motions of nearby agents from partial and noisy data. This paper asks and answers the question: "can we learn, in real-time, a nonlinear predictive model of another agent's motions?" Our online framework denoises and forecasts such dynamics using a modified …

• PO-CKAN:Physics Informed Deep Operator Kolmogorov Arnold Networks with Chunk Rational Structure

  Junyi Wu, Guang Lin · 4 novembre 2025

  We propose PO-CKAN, a physics-informed deep operator framework based on Chunkwise Rational Kolmogorov--Arnold Networks (KANs), for approximating the solution operators of partial differential equations. This framework leverages a Deep Operator Network (DeepONet) architecture that incorporates Chunkw…