Related papers: Physics informed learning of orthogonal features w…

Generalization has been one of the major challenges for learning dynamics models in model-based reinforcement learning. However, previous work on action-conditioned dynamics prediction focuses on learning the pixel-level motion and thus…

We propose a finite-element local basis-based operator learning framework for solving partial differential equations (PDEs). Operator learning aims to approximate mappings from input functions to output functions, where the latter are…

Many crucial tasks of image processing and computer vision are formulated as inverse problems. Thus, it is of great importance to design fast and robust algorithms to solve these problems. In this paper, we focus on generalized projected…

Predicting optoelectronic properties of large-scale atomistic systems under realistic conditions is crucial for rational materials design, yet computationally prohibitive with first-principles simulations. Recent neural network models have…

Avoiding over-pressurization in subsurface reservoirs is critical for applications like CO2 sequestration and wastewater injection. Managing the pressures by controlling injection/extraction are challenging because of complex heterogeneity…

We present an end-to-end framework to learn partial differential equations that brings together initial data production, selection of boundary conditions, and the use of physics-informed neural operators to solve partial differential…

This paper proposes deception as a mechanism for out-of-distribution (OOD) generalization: by learning data representations that make training data appear independent and identically distributed (iid) to an observer, we can identify stable…

Dynamic Mode Decomposition (DMD) has received increasing research attention due to its capability to analyze and model complex dynamical systems. However, it faces challenges in computational efficiency, noise sensitivity, and difficulty…

We aim to develop physics foundation models for science and engineering that provide real-time solutions to Partial Differential Equations (PDEs) which preserve structure and accuracy under adaptation to unseen geometries. To this end, we…

Fractional Laplace equations are becoming important tools for mathematical modeling and prediction. Recent years have shown much progress in developing accurate and robust algorithms to numerically solve such problems, yet most solvers for…

A fundamental problem in machine learning is to understand how neural networks make accurate predictions, while seemingly bypassing the curse of dimensionality. A possible explanation is that common training algorithms for neural networks…

In the realm of computer vision and graphics, accurately establishing correspondences between geometric 3D shapes is pivotal for applications like object tracking, registration, texture transfer, and statistical shape analysis. Moving…

Physics-based differentiable rendering (PBDR) has become an efficient method in computer vision, graphics, and machine learning for addressing an array of inverse problems. PBDR allows patterns to be generated from perceptions which can be…

In this thesis, we draw inspiration from both classical system identification and modern machine learning in order to solve estimation problems for real-world, physical systems. The main approach to estimation and learning adopted is…

Deep learning-based reconstruction of positron emission tomography(PET) data has gained increasing attention in recent years. While these methods achieve fast reconstruction,concerns remain regarding quantitative accuracy and the presence…

Solving high-dimensional Fokker-Planck (FP) equations is a challenge in computational physics and stochastic dynamics, due to the curse of dimensionality (CoD) and unbounded domains. Existing deep learning approaches, such as…

Reduced Order Models (ROMs) form essential tools across engineering domains by virtue of their function as surrogates for computationally intensive digital twinning simulators. Although purely data-driven methods are available for ROM…

A novel image matching method is proposed that utilizes learned features extracted by an off-the-shelf deep neural network to obtain a promising performance. The proposed method uses pre-trained VGG architecture as a feature extractor and…

We propose a machine learning framework to accelerate numerical computations of time-dependent ODEs and PDEs. Our method is based on recasting (generalizations of) existing numerical methods as artificial neural networks, with a set of…

We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…