Related papers: Discretization-independent multifidelity operator …

Applications in quantitative finance such as optimal trade execution, risk management of options, and optimal asset allocation involve the solution of high dimensional and nonlinear Partial Differential Equations (PDEs). The connection…

Recently, researchers have utilized neural networks to accurately solve partial differential equations (PDEs), enabling the mesh-free method for scientific computation. Unfortunately, the network performance drops when encountering a high…

Inspired by applications in optimal control of semilinear elliptic partial differential equations and physics-integrated imaging, differential equation constrained optimization problems with constituents that are only accessible through…

Finite element discretizations of problems in computational physics often rely on adaptive mesh refinement (AMR) to preferentially resolve regions containing important features during simulation. However, these spatial refinement strategies…

Operator learning aims to discover properties of an underlying dynamical system or partial differential equation (PDE) from data. Here, we present a step-by-step guide to operator learning. We explain the types of problems and PDEs amenable…

In continual learning, the primary challenge is to learn new information without forgetting old knowledge. A common solution addresses this trade-off through regularization, penalizing changes to parameters critical for previous tasks. In…

Personalization in federated learning (FL) functions as a coordinator for clients with high variance in data or behavior. Ensuring the convergence of these clients' models relies on how closely users collaborate with those with similar…

Most existing federated learning methods are unable to estimate model/predictive uncertainty since the client models are trained using the standard loss function minimization approach which ignores such uncertainties. In many situations,…

Iterative refinement -- start with a random guess, then iteratively improve the guess -- is a useful paradigm for representation learning because it offers a way to break symmetries among equally plausible explanations for the data. This…

In the pursuit of accurate experimental and computational data while minimizing effort, there is a constant need for high-fidelity results. However, achieving such results often requires significant computational resources. To address this…

Multilevel optimization has gained renewed interest in machine learning due to its promise in applications such as hyperparameter tuning and continual learning. However, existing methods struggle with the inherent difficulty of efficiently…

We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…

Distributionally robust reinforcement learning (DRRL) focuses on designing policies that achieve good performance under model uncertainties. The goal is to maximize the worst-case long-term discounted reward, where the data for RL comes…

Neural operators, as an efficient surrogate model for learning the solutions of PDEs, have received extensive attention in the field of scientific machine learning. Among them, attention-based neural operators have become one of the…

In this paper we propose a new model-based unsupervised learning method, called VarNet, for the solution of partial differential equations (PDEs) using deep neural networks (NNs). Particularly, we propose a novel loss function that relies…

Many physical and mathematical models involve random fields in their input data. Examples are ordinary differential equations, partial differential equations and integro--differential equations with uncertainties in the coefficient…

In computational physics, a longstanding challenge lies in finding numerical solutions to partial differential equations (PDEs). Recently, research attention has increasingly focused on Neural Operator methods, which are notable for their…

Public pretraining is a promising approach to improve differentially private model training. However, recent work has noted that many positive research results studying this paradigm only consider in-distribution tasks, and may not apply to…

We propose a new neural network based large eddy simulation framework for the incompressible Navier-Stokes equations based on the paradigm "discretize first, filter and close next". This leads to full model-data consistency and allows for…