Related papers: MSINO: Curvature-Aware Sobolev Optimization for Ma…

Traditional manifold learning algorithms assumed that the embedded manifold is globally or locally isometric to Euclidean space. Under this assumption, they divided manifold into a set of overlapping local patches which are locally…

Model calibration measures the agreement between the predicted probability estimates and the true correctness likelihood. Proper model calibration is vital for high-risk applications. Unfortunately, modern deep neural networks are poorly…

In this work, we develop new generalization bounds for neural networks trained on data supported on Riemannian manifolds. Existing generalization theories often rely on complexity measures derived from Euclidean geometry, which fail to…

We present a physics-informed neural network (PINN) approach for the discovery of slow invariant manifolds (SIMs), for the most general class of fast/slow dynamical systems of ODEs. In contrast to other machine learning (ML) approaches that…

Neural operators have emerged as cost-effective surrogates for expensive fluid-flow simulators, particularly in computationally intensive tasks such as permeability inversion from time-lapse seismic data, and uncertainty quantification. In…

We establish a unified theoretical framework addressing the stability, consistency, and convergence of neural networks under realistic training conditions, specifically, in the presence of non-IID data, geometric constraints, and embedded…

The ``differentiability gap'' presents a primary bottleneck in Earth system deep learning: since models cannot be trained directly on non-differentiable scientific metrics and must rely on smooth proxies (e.g., MSE), they often fail to…

Physics-Informed Neural Networks (PINNs) have emerged as a powerful framework for solving partial differential equations (PDEs), yet they often fail to achieve accurate convergence in the H1 norm, especially in the presence of boundary…

Data-driven methods have emerged as powerful tools for modeling the responses of complex nonlinear materials directly from experimental measurements. Among these methods, the data-driven constitutive models present advantages in physical…

Symbol detection for Massive Multiple-Input Multiple-Output (MIMO) is a challenging problem for which traditional algorithms are either impractical or suffer from performance limitations. Several recently proposed learning-based approaches…

Spatially referenced datasets have become increasingly prevalent across many fields, largely driven by advances in data collection methods such as satellite remote sensing. In many applications, predictions at unobserved locations are…

We propose a hybrid physics-informed machine learning framework to approximate invariant manifolds (IMs) of discrete-time dynamical systems driven by exogenous autonomous dynamics (exosystems). Such systems appear in applications ranging…

Recent experiments have shown that training trajectories of multiple deep neural networks with different architectures, optimization algorithms, hyper-parameter settings, and regularization methods evolve on a remarkably low-dimensional…

This paper proposes a physics-informed neural operator (PINO) framework for solving inverse scattering problems, enabling rapid and accurate reconstructions under diverse measurement conditions. In the proposed approach, the dielectric…

Learning-enabled control systems increasingly rely on multiple sensing modalities (e.g., vision, audio, language, etc.) for perception and decision support. A key challenge is that multi-modal sensor training dynamics are often imbalanced:…

Physics-Informed Neural Networks (PINNs) frequently encounter difficulties in accurately resolving shock waves within high-speed compressible flows, a failure largely attributed to the "gradient pathology" arising from extreme stiffness at…

This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian…

Riemannian meta-optimization provides a promising approach to solving non-linear constrained optimization problems, which trains neural networks as optimizers to perform optimization on Riemannian manifolds. However, existing Riemannian…

We propose a geometry-aware strategy for training neural preconditioners tailored to parametrized linear systems arising from the discretization of mixed-dimensional partial differential equations (PDEs). These systems are typically…

We propose a novel framework, called Markov-Lipschitz deep learning (MLDL), to tackle geometric deterioration caused by collapse, twisting, or crossing in vector-based neural network transformations for manifold-based representation…