Model Reduction and Neural Networks

Neueste Paper

• Generative Models on Analog Hardware with Dynamics

  Yu-Neng Wang, Sara Achour · 26. Juni 2026

  Analog hardware platforms such as coupled oscillators and Analog Ising Machines naturally solve differential equations at a fraction of the energy cost of digital computation, making them attractive for low-power generative modeling, yet a fundamental mismatch exists: modern generative models assume…

• ResilPhase: Plug-and-Play Phase Mapping and Noise-Resilient Macro-Trajectory Extrapolation for Diffusion Acceleration

  Qicheng Zhao, Yu Li, Qi Sun, Zheyu Yan · 26. Juni 2026

  The adoption of powerful diffusion models is hindered by their significant inference latency. Recent ``cache-then-forecast'' schemes alleviate this issue by accelerating DiTs using derivative-based polynomials, but they suffer from severe quality degradation at high acceleration ratios. Our analysis…

• Effective Covariance Dynamics in Solvable High-Dimensional GANs

  Andrew Bond, Zafer Do\u{g}an · 26. Juni 2026

  We study a solvable high-dimensional model of generative adversarial network (GAN) training in which a linear generator learns a low-dimensional subspace from data with structured latent covariance. Prior solvable GAN analyses assume unconditional signals with diagonal latent covariance; we extend t…

• Error-Conditioned Neural Solvers

  Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park · 26. Juni 2026

  Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution. Recent hybrid methods prom…

• Recovering Governing Equations from Solution Data: Identifiability Bounds for Linear and Nonlinear ODEs

  Yang Pan, Helmut B\"olcskei · 26. Juni 2026

  Learning governing equations from observed solution data is a fundamental challenge in scientific machine learning \cite{bruntonDiscoveringGoverningEquations2016,kovachkiNeuralOperatorLearning2023,longPDENetLearningPDEs2018,rudyDatadrivenDiscoveryPartial2017,raonicConvolutionalNeuralOperators2023}, …

• Kolmogorov Arnold networks (KAN) for aerodynamic prediction: a comparison with MLPs and GNNs

  Miguel Jaraiz, Fermin Gutierrez, Pablo Yeste, Miguel S\'anchez-Dom\'inguez, Eusebio Valero, Gonzalo Rubio, Lucas Lacasa · 26. Juni 2026

  Kolmogorov Arnold networks (KAN) have recently been introduced as a (deep) neural network architecture whose trainable parameters adapt the activation functions, instead of the coefficients of the affine transformations at the core of traditional architectures such as deep multilayer perceptrons (ML…

• Symplectic Neural Networks for learning Generalized Hamiltonians

  Harsh Choudhary, Vyacheslav Kungurtsev, Chandan Gupta, Melvin Leok, Georgios Korpas · 26. Juni 2026

  Hamiltonian Neural Networks (HNNs) integrate physical priors into neural models by learning a system's Hamiltonian, improving generalization and sample efficiency. Identifying the system Hamiltonian from noisy observations of state variables is a challenging task. For simulations to faithfully refle…

• When Do Conservation Laws Survive Learned Representations? Certified Horizons for Latent World Models

  Hongbo Wang · 25. Juni 2026

  We ask a representation-learning question about physical world models: when does a conservation law remain certifiable after a model learns a latent representation? A certified horizon bounds -- in advance, from measurable model defects -- how many steps a rollout provably stays on a physical invari…

• A Zeroth-Order Deep Learning Method for Fully Nonlinear Parabolic Partial Differential Equations with Unknown Coefficients

  Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou · 25. Juni 2026

  High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging. Existing deep learning solvers often rely on repeated…

• LLM-ACES: Closed-Loop Discovery of Dynamical Systems with LLM-Guided Adaptive Search

  Nikhil Abhyankar, Sha Li, Sanchit Kabra, Naren Ramakrishnan, Yulia Gel, Chandan K. Reddy · 25. Juni 2026

  Recovering governing Ordinary Differential Equations (ODEs) from data is a central challenge in modeling dynamical systems across scientific domains. Existing approaches cast discovery as a static inference problem over fixed datasets, assuming that the observed trajectories are sufficiently informa…

• A Flow-rate-conserving CNN-based Domain Decomposition Method for Blood Flow Simulations

  Simon Klaes, Axel Klawonn, Natalie Kubicki, Martin Lanser, Kengo Nakajima, Takashi Shimokawabe, Janine Weber · 25. Juni 2026

  This work aims to predict blood flow with non-Newtonian viscosity in stenosed arteries using convolutional neural network (CNN) surrogate models. An alternating Schwarz domain decomposition method is proposed which uses CNN-based subdomain solvers. A universal subdomain solver (USDS) is trained …

• Silent Failures in Physics-Informed Neural Networks: Parameter Poisoning and the Limits of Loss-Based Validation

  David McShannon, Nicholas Dietrich · 25. Juni 2026

  Physics-informed neural networks (PINNs) embed governing equations in their loss function, enabling mesh-free solutions to partial differential equations. Low training loss is treated as evidence that the learned solution is physically correct. This paper shows that assumption breaks down when encod…

• Hessian-augmented Supervised Learning for Hamilton-Jacobi-Bellman PDEs

  Mat\'ias G\'omez-Aedo, Behzad Azmi, Yuyang Huang, Dante Kalise, Karl Kunisch · 24. Juni 2026

  A data-driven method is developed for approximating value functions in deterministic optimal control problems with nonlinear control-affine dynamics. The Pontryagin Maximum Principle optimality system is solved from multiple initial conditions to generate training data consisting of values, gradient…

• Real vs. Complex Spectral Bases for Neural Operators: The Role of Green's Function Alignment

  Jason Sulskis, Sathya Ravi · 24. Juni 2026

  Fourier Neural Operators (FNO) learn solution operators of partial differential equations by parameterizing global convolutions in the complex Fourier domain. For real-valued PDE solutions, the complex FFT carries representational redundancy through conjugate symmetry. We introduce the Hartley Neura…

• Dirac-Frenkel dynamics with inertia for nonlinearly parametrized solutions of evolution problems

  Matteo Raviola, Benjamin Peherstorfer · 24. Juni 2026

  Even when Dirac-Frenkel dynamics determine a well-defined evolution in function space, the corresponding parameter dynamics can be non-unique or ill-conditioned for redundant nonlinear parametrizations such as neural networks or mixture models. We propose to add inertia to the Dirac-Frenkel dynamics…

• Structural Kolmogorov-Arnold Convolutions: Learnable Function on the Values or the Filter Shape as Parameter-Efficient Alternative to Per-Edge Convolutional KANs

  Stefano Mereu, Oleksandr Kuznetsov, Gabriele Marchello, Alessandro Galdelli, Emanuele Frontoni, Adriano Mancini, Ferdinando Cannella · 24. Juni 2026

  Convolutional Kolmogorov--Arnold Networks (KANs) replace the fixed weights of a convolutional kernel with learnable univariate functions. The dominant formulation attaches one such function to every kernel entry and lets it act on pixel values, expressive but parameter-heavy and prone to overfitting…

• Neural Network-Based Parametric Model Reduction for Predicting Turbulent Flow for Different Vehicle Geometries

  Kazuto Ando, Rahul Bale, Akiyoshi Kuroda, Makoto Tsubokura · 24. Juni 2026

  Numerical simulations in industrial applications often require performing numerous high-precision computations parameterized by specific experimental conditions. For instance, in vehicle body design, aerodynamic simulations are essential for evaluating the aerodynamic characteristics of various prop…

• Learning the Koopman Operator using Attention Free Transformers

  Mohammed Nagdi, Evangelos-Marios Nikolados, Alexey Yermakov, Mars Gao, Nathan Kutz, Filippo Menolascina · 24. Juni 2026

  Learning Koopman operators with autoencoders enables linear prediction in a latent space, but long-horizon rollouts often drift off the learned manifold, leading to phase and amplitude errors on systems with switching, continuous spectra, or strong transients. We introduce two complementary componen…

• A Physics-Informed Fourier-Wavelet Transformer for Multiscale Computational Fluid Dynamics Surrogate Modeling

  Somyajit Chakraborty, Ming Pan, Xizhong Chen · 24. Juni 2026

  Physics-informed surrogate models can accelerate computational fluid dynamics simulations. However, many existing methods reproduce global flow patterns more reliably than localized multiscale structures. This study presents a physics-informed Fourier-wavelet transformer for next-step velocity-field…

• SPADE: Structure-Prior Adaptive Decision Estimation

  Yifan Wang · 23. Juni 2026

  Physical-structure priors such as conservation laws, Hamiltonian forms, and symmetries can improve scientific machine learning when correct, but can degrade predictions when misspecified. Existing methods usually enforce a chosen structure or tune a soft penalty, without a calibrated rule for decidi…

• TF-SNO: Time-Frequency Gated Spectral Neural Operators for Learning Non-Stationary Partial Differential Equations

  Yitian Zhou, Chaoning Zhang, Zhenzhen Huang, Haoxuan Yu, Jiaquan Zhang, Yiran Li, Fan Mo, Kuien Liu, Jie Zou, Caiyan Qin, Yang Yang · 23. Juni 2026

  Non-stationary partial differential equations (PDEs) arise throughout scientific computing, where the dominant frequency content and energy distribution can drift over time. While efficient in PDE solving, many spectral neural operators apply a shared spectral response across rollout stages, leading…

• LSTM Variants for Chaotic Dynamical Systems: An Empirical Study on the Lorenz Attractor

  Ruslan Gokhman · 23. Juni 2026

  Forecasting chaotic dynamical systems such as the Lorenz attractor is notoriously difficult: small numerical errors are amplified exponentially over long autoregressive rollouts. We study seven recurrent and convolutional architectures for the AI-DEEDS 2026 Chaotic Systems Challenge: a vanilla LSTM,…

• Inverse Problem for Partial Differential Equations with Jump Discontinuities in Coefficients by Two-stage Physics-Informed Deep Learning and Statistical Mixture Models

  Zhikun Zhang, Guanyu Pan, Xiangjun Wang, Yong Xu, Guangtao Zhang · 23. Juni 2026

  This work proposes a two-stage physics-informed deep learning framework that combines neural-network-based sampling with statistical inference and constrained parameter refinement. In the first stage, a dual-network physics-informed architecture is used, where a main-network approximates the PDE sol…

• NewPINNs: Physics-Informing Neural Networks Using Conventional Solvers for Partial Differential Equations

  Satish Chandran, Maedeh Makki, Maziar Raissi, Adrien Grenier, Behzad Mohebbi · 23. Juni 2026

  We introduce NewPINNs, a physics-informing learning framework that couples neural networks with conventional numerical solvers for solving differential equations. Rather than enforcing governing equations and boundary conditions through residual-based loss terms, NewPINNs integrates the solver direc…

• Physics-Informed Neural Networks for Computing the Morse Index of the Critical Catenoid

  Miraj Samarakkody · 23. Juni 2026

  The Morse index of a free boundary minimal surface is encoded in its Jacobi-Steklov spectrum, and we test how faithfully a physics-informed neural network (PINN) reproduces that spectrum on a problem whose answer is already known in closed form. The benchmark is the critical catenoid in the unit bal…