Related papers: Hybrid Iterative Neural Low-Regularity Integrator …

Deep learning-based hybrid iterative methods (DL-HIMs) integrate classical numerical solvers with neural operators, utilizing their complementary spectral biases to accelerate convergence. Despite this promise, many DL-HIMs stagnate at…

This work proposes a hybrid modeling framework based on recurrent neural networks (RNNs) and the finite element (FE) method to approximate model discrepancies in time dependent, multi-fidelity problems, and use the trained hybrid models to…

We study a novel class of algorithms for solving model-free feedback optimization problems in dynamical systems. The key novelty is the introduction of \emph{persistent resetting learning integrators} (PRLI), which are integrators that are…

Certified robustness is a critical property for deploying neural networks (NN) in safety-critical applications. A principle approach to achieving such guarantees is to constrain the global Lipschitz constant of the network. However,…

Despite the remarkable progress facilitated by learning-based stereo-matching algorithms, disparity estimation in low-texture, occluded, and bordered regions still remains a bottleneck that limits the performance. To tackle these…

Current test- or compression-time adaptation image compression (TTA-IC) approaches, which leverage both latent and decoder refinements as a two-step adaptation scheme, have potentially enhanced the rate-distortion (R-D) performance of…

Iterative algorithms solve problems by taking steps until a solution is reached. Models in the form of Deep Thinking (DT) networks have been demonstrated to learn iterative algorithms in a way that can scale to different sized problems at…

In this paper, we consider the numerical solution of the continuous disordered nonlinear Schr\"odinger equation, which contains a spatial random potential. We address the finite time accuracy order reduction issue of the usual numerical…

We demonstrate that applying an eventual decay to the learning rate (LR) in empirical risk minimization (ERM), where the mean-squared-error loss is minimized using standard gradient descent (GD) for training a two-layer neural network with…

Implicit Neural Representations (INRs) have emerged as a powerful tool for geometric representation, yet their suitability for physics-based simulation remains underexplored. While metrics like Hausdorff distance quantify surface…

This paper fortifies the recently introduced hierarchical-optimization recursive least squares (HO-RLS) against outliers which contaminate infrequently linear-regression models. Outliers are modeled as nuisance variables and are estimated…

This work presents a hybrid modeling approach to data-driven learning and representation of unknown physical processes and closure parameterizations. These hybrid models are suitable for situations where the mechanistic description of…

Learned Iterative Shrinkage-Thresholding Algorithm (LISTA) introduces the concept of unrolling an iterative algorithm and training it like a neural network. It has had great success on sparse recovery. In this paper, we show that adding…

This paper presents a novel holistic deep learning framework that simultaneously addresses the challenges of vulnerability to input perturbations, overparametrization, and performance instability from different train-validation splits. The…

Binary Neural Networks are a promising technique for implementing efficient deep models with reduced storage and computational requirements. The training of these is however, still a compute-intensive problem that grows drastically with the…

A feedforward neural network, including hidden layers, motivated by nonlinear functions (such as Tanh, ReLU, and Sigmoid functions), exhibits uniform approximation properties in Sobolev space, and discontinuous neural networks can reduce…

Neural networks are predominantly trained using gradient-based methods, yet in many applications their final predictions remain far from the accuracy attainable within the model's expressive capacity. We introduce Linearized Subspace…

Optimization problems characterized by both discrete and continuous variables are common across various disciplines, presenting unique challenges due to their complex solution landscapes and the difficulty of navigating mixed-variable…

Non-linear differential equations are a fundamental tool to describe different phenomena in nature. However, we still lack a well-established method to tackle stiff differential equations. Here we present a machine learning framework to…

The use of Implicit Neural Representation (INR) through a hash-table has demonstrated impressive effectiveness and efficiency in characterizing intricate signals. However, current state-of-the-art methods exhibit insufficient…