Model Reduction and Neural Networks

Derniers papiers

• Tokenised Flow Matching for Hierarchical Simulation Based Inference

  Giovanni Charles, Cosmo Santoni, Seth Flaxman, Elizaveta Semenova · 23 avril 2026

  The cost of simulator evaluations is a key practical bottleneck for Simulation Based Inference (SBI). In hierarchical settings with shared global parameters and exchangeable site-level parameters and observations, this structure can be exploited to improve simulation efficiency. Existing hierarchica…

• Machine learning moment closure models for the radiative transfer equation IV: enforcing symmetrizable hyperbolicity in two dimensions

  Juntao Huang · 23 avril 2026

  This is our fourth work in the series on machine learning (ML) moment closure models for the radiative transfer equation (RTE). In the first three papers of this series, we considered the RTE in slab geometry in 1D1V (i.e. one dimension in physical space and one dimension in angular space), and intr…

• Fast Amortized Fitting of Scientific Signals Across Time and Ensembles via Transferable Neural Fields

  Sophia Zorek, Kushal Vyas, Yuhao Liu, David Lenz, Tom Peterka, Guha Balakrishnan · 23 avril 2026

  Neural fields, also known as implicit neural representations (INRs), offer a powerful framework for modeling continuous geometry, but their effectiveness in high-dimensional scientific settings is limited by slow convergence and scaling challenges. In this study, we extend INR models to handle spati…

• AI models of unstable flow exhibit hallucination

  Ramdhan Wibawa, Birendra Jha · 23 avril 2026

  We report the first systematic evidence of hallucination in AI models of fluid dynamics, demonstrated in the canonical problem of hydrodynamically unstable transport known as viscous fingering. AI-based modeling of flow with instabilities remains challenging because rapidly evolving, multiscale fing…

• Structure-Aware Variational Learning of a Class of Generalized Diffusions

  Yubin Lu, Xiaofan Li, Chun Liu, Qi Tang, Yiwei Wang · 23 avril 2026

  Learning the underlying potential energy of stochastic gradient systems from partial and noisy observations is a fundamental problem arising in physics, chemistry, and data-driven modeling. Classical approaches often rely on direct regression of governing equations or velocity fields, which can be s…

• Control Consistency Losses for Diffusion Bridges

  Samuel Howard, Nikolas N\"usken, Jakiw Pidstrigach · 23 avril 2026

  Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the unconditioned dynamics rarely reach the terminal state. In this work,…

• Artifacts of Numerical Integration in Learning Dynamical Systems

  Bing-Ze Lu, Richard Tsai · 23 avril 2026

  In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimization problem over a chosen function class. However, in the optimization procedure, prediction data from generic dynamics re…

• Physics-Guided Dimension Reduction for Simulation-Free Operator Learning of Stiff Differential--Algebraic Systems

  Huy Hoang Le, Haoguang Wang, Christian Moya, Marcos Netto, Guang Lin · 23 avril 2026

  Neural surrogates for stiff differential-algebraic equations (DAEs) face two key challenges: soft-constraint methods leave algebraic residuals that stiffness amplifies into large errors, while hard-constraint methods require trajectory data from computationally expensive stiff integrators. We introd…

• Fourier Weak SINDy: Spectral Test Function Selection for Robust Model Identification

  Zhiheng Chen, Urban Fasel, Anastasia Bizyaeva · 23 avril 2026

  We introduce Fourier Weak SINDy, a minimal noise-robust and interpretable derivative-free equation learning method that combines weak-form sparse equation learning with spectral density estimation for data-driven test function selection. By using orthogonal sinusoidal test functions inspired by thei…

• FlowForge: A Staged Local Rollout Engine for Flow-Field Prediction

  Xiaowen Zhang, Ziming Zhou, Fengnian Zhao, David L. S. Hung · 22 avril 2026

  Deep learning surrogates for CFD flow-field prediction often rely on large, complex models, which can be slow and fragile when data are noisy or incomplete. We introduce FlowForge, a staged local rollout engine that predicts future flow fields by compiling a locality-preserving update schedule and e…

• Safety-Critical Contextual Control via Online Riemannian Optimization with World Models

  Tongxin Li · 22 avril 2026

  Modern world models are becoming too complex to admit explicit dynamical descriptions. We study safety-critical contextual control, where a Planner must optimize a task objective using only feasibility samples from a black-box Simulator, conditioned on a context signal $\xi_t$. We develop a sample-b…

• Debiased neural operators for estimating functionals

  Konstantin Hess, Dennis Frauen, Niki Kilbertus, Stefan Feuerriegel · 22 avril 2026

  Neural operators are widely used to approximate solution maps of complex physical systems. In many applications, however, the goal is not to recover the full solution trajectory, but to summarize the solution trajectory via a scalar target quantity (e.g., a functional such as time spent in a target …

• Skillful Global Ocean Emulation and the Role of Correlation-Aware Loss

  Niraj Agarwal, Timothy A. Smith, Sergey Frolov, Laura C. Slivinski · 22 avril 2026

  Machine learning emulators have shown extraordinary skill in forecasting atmospheric states, and their application to global ocean dynamics offers similar promise. Here, we adapt the GraphCast architecture into a dedicated ocean-only emulator, driven by prescribed atmospheric conditions, for medium-…

• A neural operator framework for data-driven discovery of stability and receptivity in physical systems

  Chengyun Wang, Liwei Chen, Nils Thuerey · 22 avril 2026

  Understanding how complex systems respond to perturbations, such as whether they will remain stable or what their most sensitive patterns are, is a fundamental challenge across science and engineering. Traditional stability and receptivity (resolvent) analyses are powerful but rely on known equation…

• Beyond Bellman: High-Order Generator Regression for Continuous-Time Policy Evaluation

  Yaowei Zheng, Richong Zhang, Shenxi Wu, Shirui Bian, Haosong Zhang, Li Zeng, Xingjian Ma, Yichi Zhang · 22 avril 2026

  We study finite-horizon continuous-time policy evaluation from discrete closed-loop trajectories under time-inhomogeneous dynamics. The target value surface solves a backward parabolic equation, but the Bellman baseline obtained from one-step recursion is only first-order in the grid width. We estim…

• Local Linearity of LLMs Enables Activation Steering via Model-Based Linear Optimal Control

  Julian Skifstad, Xinyue Annie Yang, Glen Chou · 22 avril 2026

  Inference-time LLM alignment methods, particularly activation steering, offer an alternative to fine-tuning by directly modifying activations during generation. Existing methods, however, often rely on non-anticipative interventions that ignore how perturbations propagate through transformer layers …

• On the Interpolation Effect of Score Smoothing in Diffusion Models

  Zhengdao Chen · 21 avril 2026

  Diffusion models have achieved remarkable progress in various domains with an intriguing ability to produce new data that do not exist in the training set. In this work, we study the hypothesis that such creativity arises from the neural network backbone learning a smoothed version of the empirical …

• FlowRefiner: Flow Matching-Based Iterative Refinement for 3D Turbulent Flow Simulation

  Yilong Dai, Yiming Sun, Yiheng Chen, Shengyu Chen, Xiaowei Jia, Runlong Yu · 21 avril 2026

  Accurate autoregressive prediction of 3D turbulent flows remains challenging for neural PDE solvers, as small errors in fine-scale structures can accumulate rapidly over rollout. In this paper, we propose FlowRefiner, a flow matching-based iterative refinement framework for 3D turbulent flow simulat…

• Learning the Riccati solution operator for time-varying LQR via Deep Operator Networks

  Jun Chen, Umberto Biccari, Junmin Wang · 21 avril 2026

  We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator surrogate. Instead of solving a nonlinear matrix-valued differential equation for each new system ins…

• Neural Shape Operator Surrogates -- Expression Rate Bounds

  Helmut Harbrecht, Christoph Schwab · 21 avril 2026

  We prove error bounds for operator surrogates of solution operators for partial differential and boundary integral equations on families of domains which are diffeomorphic to one common reference (or latent) domain $D_{ref}$. The pullback of the PDE to $D_{ref}$ via affine-parametric shape encoding …

• Dissipative Latent Residual Physics-Informed Neural Networks for Modeling and Identification of Electromechanical Systems

  Youyuan Long, Gokhan Solak, Arash Ajoudani · 21 avril 2026

  Accurate dynamical modeling is essential for simulation and control of embodied systems, yet first-principles models of electromechanical systems often fail to capture complex dissipative effects such as joint friction, stray losses, and structural damping. While residual-learning physics-informed n…

• Singularity Formation: Synergy in Theoretical, Numerical and Machine Learning Approaches

  Yixuan Wang · 21 avril 2026

  This thesis develops numerical and theoretical approaches for understanding and analyzing singularity formation in Partial Differential Equations (PDEs). The singularity formation in the Navier-Stokes Equation (NSE) is famously challenging as one of the seven Clay Prize problems. Unlike simpler equa…

• Neural Network-Based Score Estimation in Diffusion Models: Optimization and Generalization

  Yinbin Han, Meisam Razaviyayn, Renyuan Xu · 21 avril 2026

  Diffusion models have become a leading paradigm in generative AI, with score estimation via denoising score matching as a central component. While recent theory provides strong statistical guarantees, it typically relies on algorithm-agnostic assumptions and treats empirical risk minimization as if …

• XRePIT: A deep learning-computational fluid dynamics hybrid framework implemented in OpenFOAM for fast, robust, and scalable unsteady simulations

  Shilaj Baral, Youngkyu Lee, Sangam Khanal, Joongoo Jeon · 21 avril 2026

  Autoregressive neural surrogates offer computational acceleration for fluid dynamics but inherently suffer from error accumulation and non-physical drift during long-term rollouts. Although hybrid strategies combining surrogate models and physics-based solvers have been proposed, they are limited to…

• Faster by Design: Interactive Aerodynamics via Neural Surrogates Trained on Expert-Validated CFD

  Nicholas Thumiger, Andrea Bartezzaghi, Mattia Rigotti, Cezary Skura, Thomas Frick, Elisa Serioli, Fabrizio Arbucci, A. Cristiano I. Malossi · 21 avril 2026

  Computational Fluid Dynamics (CFD) is central to race-car aerodynamic development, yet its cost -- tens of thousands of core-hours per high-fidelity evaluation -- severely limits the design space exploration feasible within realistic budgets. AI-based surrogate models promise to alleviate this bottl…