arXiv Machine Learning

Neural Discovery of Memory and Nonlocal Kernels in Integro-Differential Equations with Constrained Kolmogorov--Arnold Networks

arXiv:2607. 11110v1 Announce Type: new Abstract: Discovering the memory or nonlocal kernel governing an integro-differential equation (IDE) from sparse and noisy observations is an ill-posed inverse problem.

arXiv Machine Learning

Jul 23

PG-KINN: A Physics-Informed Petrov-Galerkin Kolmogorov-Arnold Network for Solving Forward and Inverse PDEs

arXiv:2607. 20378v1 Announce Type: new Abstract: Physics-informed learning of partial differential equations (PDEs) has been dominated by multilayer perceptrons (MLPs), whose spectral bias and dense parameterization limit both accuracy and interpretability.

By Amirhossein Sadr, Nima Soltani, Vahideh Moghtadaiee, Aida Pakniyat, Dara Rahmati, Saeid Gorgin

benchmarks safety

arXiv Machine Learning

Jul 30

PIKS: Universal Physics-Informed Kernel Methods

arXiv:2607. 27062v1 Announce Type: cross Abstract: Physics-informed machine learning incorporates physical principles --often expressed via differential operators-- into data-driven models.

By Joachim Bona-Pellissier, Giacomo Meanti, Matteo Santacesaria, Lorenzo Rosasco

arXiv Machine Learning

Jun 5

Effective Dimensionality as an Operator Invariant for Physics-Preserving Constraint Adaptation in Physics-Informed Neural Networks

arXiv:2606. 06171v1 Announce Type: cross Abstract: Physics-Informed Neural Networks inherently suffer from task interference because they rely on a shared parameter space to satisfy both governing differential equations and boundary conditions.

By Cornelius Otchere, Michael Shields

fine-tuning

arXiv Machine Learning

6d ago

Kernel Methods for Learning Operators with Multiple Inputs and Outputs

arXiv:2608. 11831v1 Announce Type: new Abstract: Learning mappings between infinite-dimensional objects is a central challenge in scientific machine learning.

By Adrien Weihs, Chunyang Liao, Jingmin Sun, Hayden Schaeffer

benchmarks

arXiv Machine Learning

Jun 19

A deep learning framework for jointly solving transient Fokker-Planck equations with arbitrary parameters and initial distributions

arXiv:2604. 06001v2 Announce Type: replace-cross Abstract: Efficiently solving the Fokker-Planck equation (FPE) is central to analyzing complex parameterized stochastic systems.

By Xiaolong Wang, Jing Feng, Qi Liu, Chengli Tan, Yuanyuan Liu, Yong Xu

multimodal

arXiv Machine Learning

Jun 25

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

arXiv:2606. 24999v1 Announce Type: new Abstract: 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.

By Yanwei Jia, Du Ouyang, Huy\^en Pham, Xun Yu Zhou

reinforcement-learning safety

arXiv Machine Learning

Jun 30

Learning from samples: inverse problems over measures

arXiv:2505. 07124v3 Announce Type: replace Abstract: We study inverse problems where an unknown potential is observed only through samples from the measure it induces by a convex variational principle.

By Francisco Andrade, Gabriel Peyr\'e, Clarice Poon

arXiv Machine Learning

Jun 30

A Distributionally Robust Framework for Learned Reconstructions in Inverse Problems

arXiv:2606. 30230v1 Announce Type: cross Abstract: Learned reconstruction operators for inverse problems are typically trained under a fixed noise model, and generalize poorly when the distribution during testing differs from the one assumed during training.

By Floor van Maarschalkerwaart, Subhadip Mukherjee, Christoph Brune, Marcello Carioni

safety

arXiv AI

Jun 30

Physics-Informed Distillation of Diffusion Models for PDE-Constrained Generation

arXiv:2505. 22391v2 Announce Type: replace-cross Abstract: Modeling physical systems in a generative manner offers several advantages, including the ability to handle partial observations, generate diverse solutions, and address both forward and inverse problems.

By Yi Zhang, Peng Wang, Difan Zou

diffusion efficiency benchmarks

arXiv Machine Learning

Jun 11

Structure-Preserving Neural Surrogates with Tractable Uncertainty Quantification

arXiv:2606. 11650v1 Announce Type: new Abstract: Recent advances in scientific machine learning provide a means of near-real-time solution to partial differential equations (PDEs), but lack the theoretical underpinnings of conventional simulators that support contemporary verification and validation.

By Handi Zhang, Adrienne M. Propp, Brooks Kinch, Houman Owhadi, Nathaniel Trask

llms

arXiv Machine Learning

Jun 5

Function-Space Priors for Bayesian Neural ODEs with Application to Vessel Trajectory Prediction

arXiv:2606. 06351v1 Announce Type: cross Abstract: Vessel trajectory prediction from Automatic Identification System (AIS) data is essential for maritime situational awareness, yet it remains challenging due to irregular sampling, missing reports, and complex dynamics.

By Jaeyeong Lee, Wonmo Koo, Heeyoung Kim

arXiv AI

Jun 2

Physics-Informed Deep Learning for Entropy Prediction in Heterogeneous Systems: Thermodynamic and Information-Theoretic Case Studies

arXiv:2606. 01179v1 Announce Type: cross Abstract: Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems.

By Biswajeet Sahoo, Debadutta Patra

diffusion

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