Model Reduction and Neural Networks

Derniers papiers

• Flow Learners for PDEs: Toward a Physics-to-Physics Paradigm for Scientific Computing

  Yilong Dai, Shengyu Chen, Xiaowei Jia, Runlong Yu · 3 juin 2026

  Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive. Generative AI has transformed language, vision, and protein science, but learned PDE solvers have not undergone a comparable shift. Existi…

• Oscillatory State-Space Models as Inductive Biases for Physics-Informed Neural PDE Solvers

  Abhishek Chandra, Taniya Kapoor · 3 juin 2026

  Solving time-dependent partial differential equations (PDEs) is an important problem in computational science and engineering. Physics-informed neural networks (PINNs) learn PDE solutions from governing equations. However, accurately capturing temporal evolution remains challenging. Recent sequence-…

• Let There Be Light: Reflection, Refraction and Scattering for Neural Operators

  Keke Wu, Yixuan Zhang, Jingrun Chen · 3 juin 2026

  Neural operators learn mappings between infinite-dimensional function spaces and provide a data-driven surrogate modeling paradigm for parametric partial differential equations (PDEs). Existing architectures typically obtain expressivity by parameterizing integral kernels in prescribed transform dom…

• Samudra 2: Scaling Ocean Emulators across Resolutions

  Yuan Yuan, Jesse Rusak, Alexander Merose, Adam Subel, Pavel Perezhogin, Alistair Adcroft, Carlos Fernandez-Granda, Laure Zanna · 3 juin 2026

  Ocean general circulation models (OGCMs) are essential to climate science but computationally expensive, limiting ensemble size and forcing scenarios. Neural emulators promise orders-of-magnitude speedups, yet existing ocean emulators have not combined fine spatial resolution with multi-year autoreg…

• APIC: Amortized Physics-Informed Calibration using Neural Processes

  Aishwarya Venkataramanan, Sai Karthikeya Vemuri, Joachim Denzler · 3 juin 2026

  Physics models are inherently imperfect due to misspecified or missing mechanisms, resulting in systematic discrepancies between model predictions and real-world observations. The Kennedy-O'Hagan (KOH) framework addresses this issue through explicit discrepancy modeling. However, its non-amortized, …

• A Quantitative Approximation Framework for Flow Distillation in Diffusion Models

  Weiguo Gao, Ming Li, Lei Shi, Hanfei Zhou · 3 juin 2026

  We develop a quantitative approximation framework for diffusion distillation, viewing few-step sampling as error propagation under compositions of learned flow maps. Focusing on trajectory distillation for the probability-flow ODE, we show that local approximation errors can be strongly amplified in…

• A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Model

  Jinchao Feng, Sui Tang · 3 juin 2026

  In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch-Tadmor model based on observed trajectory data. The model under consideration is governed by a class of semilinear evolution equations, where the interaction kernel defines a normalized, stat…

• Correcting Neural Operator Spectral Bias via Diffusion Posterior Sampling with Sparse Observations

  Niccol\`o Perrone, Fanny Lehmann, Stefania Fresca, Filippo Gatti · 3 juin 2026

  Neural operator surrogates (NO) approximate PDE solutions orders of magnitude faster than numerical solvers, but suffer from spectral bias: high-frequency content is systematically attenuated, limiting reliability where fine-scale structure matters. Sparse sensor measurements of the field are often …

• EqGINO: Equivariant Geometry-Informed Fourier Neural Operators for 3D PDEs

  Sungwon Kim, Juho Song, Seungmin Shin, Guimok Cho, Sangkook Kim, Chanyoung Park · 3 juin 2026

  Deep learning surrogates for 3D Partial Differential Equations (PDEs) often fail to generalize across geometric transformations because they depend heavily on specific coordinate systems. While equivariant networks offer a solution, they typically rely on local operations in the spatial domain, maki…

• Are LLMs Ready for Neural-integrated Mechanistic Modeling? A Benchmark and Agentic Framework

  Zihan Guan, Rituparna Datta, Mengxuan Hu, Shunshun Liu, Aiying Zhang, Prasanna Balachandran, Sheng Li, Anil Vullikanti · 2 juin 2026

  Large language models (LLMs) have shown promise in constructing mechanistic models from data. However, existing evaluations largely focus on simplified settings and fail to capture the complexity of real-world scientific modeling. In practice, such modeling often involves neural-integrated formulati…

• Accelerating physics-informed neural networks for full waveform inversion using a hybrid quantum-classical finite-basis architecture

  Hoang Anh Nguyen, Divakar Vashisth, Ali Tura · 2 juin 2026

  Full waveform inversion (FWI) reconstructs heterogeneous material properties from receiver data but remains computationally demanding. Physics-informed neural networks (PINNs) and their domain-decomposed variants (FBPINNs) offer a mesh-free alternative but face convergence challenges when representi…

• Learning Implicit Bias in Generative Spaces for Accelerating Protein Dynamics Emulation

  Kaihui Cheng, Zhiqiang Cai, Wenkai Xiang, Zhihang Hu, Siyu Zhu, Tzuhsiung Yang, Yuan Qi · 2 juin 2026

  Generative emulators of protein dynamics produce plausible trajectories at a fraction of the cost of molecular dynamics, but they inherit their training distribution and tend to revisit known states rather than reach rare ones under long-horizon extrapolation. Inspired by classical enhanced sampling…

• Learning Chaotic Dynamics through Second-Order Geometric Supervision

  Shinhoo Kang, Hai V. Nguyen, Tan Bui-Thanh · 2 juin 2026

  Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics. Trajectory (zero-order) and Jacobian (first-order) matching supervise the values and tangent structure of the vector fi…

• Physics-Guided Recurrent State-Space Neural Networks for Multi-Step Prediction

  Ruiyuan Li, Ajay Seth, Manon Kok · 2 juin 2026

  State-space models are traditionally based on physical knowledge, but multi-step predictions from these physical models can be poor due to model inaccuracy. Black-box deep learning has shown promise as an alternative. However, these methods rely on the availability of large datasets and potentially …

• Explainable deep reinforcement learning reveals energy-efficient control strategies for turbulent drag reduction

  Federica Tonti, Ricardo Vinuesa · 2 juin 2026

  We propose a method combining Multi-Agent Deep Reinforcement Learning (MARL) and eXplainable Deep Learning (XDL) to reduce drag in wall-bounded turbulent flows. Taking as a baseline the results of training agents directly targeting wall-shear stress and opposition control, three SHAP-guided approach…

• DASH: Dual-Branch Score Distillation for Guidance-Calibrated Compact Diffusion Models

  Abdullah Al Shafi, Kazi Saeed Alam, Sk Imran Hossain, Engelbert Mephu Nguifo · 2 juin 2026

  Parameter compression of class-conditional diffusion models reveals an underexplored limitation in output-level distillation: the unconditional score branch remains unsupervised, leaving the classifier-free guidance gap underdetermined in the student. This gap, amplified at every denoising step, adm…

• Symmetric Hermite quadrature-based balanced truncation for learning linear dynamical systems from derivative data

  Sean Reiter, Steffen W. R. Werner · 2 juin 2026

  Data-driven reduced-order modeling is an essential component in the computer-aided design of control systems. In this work, we present a novel symmetric Hermite formulation of the quadrature-based balanced truncation algorithm that constructs linear reduced-order models from evaluations of the full-…

• Is Zero-Shot Super-Resolution Possible in Operator Learning?

  Unique Subedi, Ambuj Tewari · 2 juin 2026

  Neural operators are often reported to exhibit zero-shot super-resolution, a phenomenon in which a model trained on coarse grids produces accurate predictions on finer testing grids without additional retraining. Despite strong empirical evidence, the theoretical foundations of this phenomenon remai…

• Emergent Transfer of a Physics Foundation Model from Simulation to Laboratory Turbulence

  Payel Mukhopadhyay, Stefan S. Nixon, Romain Watteaux, Michael McCabe, Alberto Bietti, Kyunghyun Cho, Cristiana Diaconu, Irina Espejo Morales, David Fouhey, Siavash Golkar, Tom Hehir, Shirley Ho, Jake Kovalic, Geraud Krawezik, Francois Lanusse, Tanya Marwah, Rudy Morel, Mariel Pettee, Helen Qu, Jeff Shen, Hadi Sotoudeh, Stuart B. Dalziel, Miles Cranmer · 2 juin 2026

  Whether physics foundation models can be usefully deployed on laboratory experiments remains an open question for scientific machine learning (ML). We test this question on the Rayleigh-Taylor instability (RTI), a ubiquitous and demanding fluid instability seen from tabletop flows to supernova explo…

• Sharpness-Aware Hybrid Model Learning for Architecture-Agnostic Parameter Estimation

  Naoya Takeishi · 2 juin 2026

  Hybrid modeling, the combination of machine learning models and scientific mathematical models, enables flexible and robust data-driven prediction with partial interpretability. However, the unknown parameters of the scientific model cannot necessarily be estimated properly, since the flexibility of…

• A Per-Component Diagnostic Protocol for Neural HJB-PIDE Solvers under Control-Dependent L\'evy Jumps

  R. Drissi · 2 juin 2026

  We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent L\'evy jumps, targeting a general failure mode of neural PDE methods: a learned solution can match headline scalar diagnostics while miscomputing an operator inside its training loss. The p…

• Knowledge-Informed Kernel State Reconstruction from Heterogeneous Partial Observations

  Luca Muscarnera, Silas Ruhrberg Est\'evez, Samuel Holt, Evgeny Saveliev, Mihaela van der Schaar · 2 juin 2026

  Real-world scientific systems are rarely observed through complete, regularly sampled state trajectories. Instead, measurements are often partial, noisy, and heterogeneous, providing fragmented views of latent dynamical states. We introduce MAAT (Model Aware Approximation of Trajectories), a framewo…

• Physics-Informed Residuals for Adaptive Mesh Refinement in Finite-Difference PDE Solvers

  Henry Kasumba, Ronald Katende · 2 juin 2026

  Classical finite-difference solvers remain reliable tools for partial differential equations, but their efficiency depends on where mesh resolution is placed. Uniform refinement can waste degrees of freedom when solution difficulty is localised near sharp gradients, fronts, oscillations, or constrai…

• Taming the Loss Landscape of PINNs with Noisy Feynman-Kac Supervision: Operator Preconditioning and Non-Asymptotic Error Bounds

  Nathanael Tepakbong, Hanyu Hu, Chengyu Liu, Xiang Zhou · 2 juin 2026

  Physics-Informed Neural Networks (PINNs) often train slowly or fail to converge on challenging partial differential equations (PDEs), a behavior recently linked to severely ill-conditioned loss landscapes inherited from the underlying differential operator. We study PINNs augmented with a pointwise …

• Cellular Sheaf Neural Operators for Structure-Preserving Surrogate Modeling of Constrained PDEs

  Lennon J. Shikhman, Shane Gilbertie · 2 juin 2026

  Neural operators provide fast surrogate models for PDE simulations, but standard architectures often treat geometry and discretization as secondary to field data. Physical states are usually represented as grid-channel stacks, even when different quantities naturally belong on vertices, edges, faces…