Related papers: Bilevel optimization for learning hyperparameters:…
We propose a new type of multilevel method for solving eigenvalue problems based on Newton iteration. With the proposed iteration method, solving eigenvalue problem on the finest finite element space is replaced by solving a small scale…
Data selection improves computational efficiency by choosing informative subsets of training samples. However, existing methods ignore the compute budget, treating data selection and importance evaluation independently of compute budget…
In this paper, we propose forward and backward stochastic differential equations (FBSDEs) based deep neural network (DNN) learning algorithms for the solution of high dimensional quasilinear parabolic partial differential equations (PDEs),…
Variational regularization methods are commonly used to approximate solutions of inverse problems. In recent years, model-based variational regularization methods have often been replaced with data-driven ones such as the fields-of-expert…
Bilevel optimization has arisen as a powerful tool for many machine learning problems such as meta-learning, hyperparameter optimization, and reinforcement learning. In this paper, we investigate the nonconvex-strongly-convex bilevel…
When training deep learning models, the performance depends largely on the selected hyperparameters. However, hyperparameter optimization (HPO) is often one of the most expensive parts of model design. Classical HPO methods treat this as a…
This paper studies numerical solutions for parameterized partial differential equations (P-PDEs) with deep learning (DL). P-PDEs arise in many important application areas and the computational cost using traditional numerical schemes can be…
We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…
We present a geometric multilevel optimization approach that smoothly incorporates box constraints. Given a box constrained optimization problem, we consider a hierarchy of models with varying discretization levels. Finer models are…
This paper aims to devise an adaptive neural network basis method for numerically solving a second-order semilinear partial differential equation (PDE) with low-regular solutions in two/three dimensions. The method is obtained by combining…
Bayesian optimization is popular for optimizing time-consuming black-box objectives. Nonetheless, for hyperparameter tuning in deep neural networks, the time required to evaluate the validation error for even a few hyperparameter settings…
The numerical solution of differential equations using machine learning-based approaches has gained significant popularity. Neural network-based discretization has emerged as a powerful tool for solving differential equations by…
Although Gaussian processes (GPs) with deep kernels have been successfully used for meta-learning in regression tasks, its uncertainty estimation performance can be poor. We propose a meta-learning method for calibrating deep kernel GPs for…
Phase recovery from the bispectrum is a central problem in speckle interferometry which can be posed as an optimization problem minimizing a weighted nonlinear least-squares objective function. We look at two different formulations of the…
We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of…
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…
We present the Deep Picard Iteration (DPI) method, a new deep learning approach for solving high-dimensional partial differential equations (PDEs). The core innovation of DPI lies in its use of Picard iteration to reformulate the typically…
This paper introduces a computationally efficient algorithm in system theory for solving inverse problems governed by linear partial differential equations (PDEs). We model solutions of linear PDEs using Gaussian processes with priors…
Bayesian methods in machine learning, such as Gaussian processes, have great advantages com-pared to other techniques. In particular, they provide estimates of the uncertainty associated with a prediction. Extending the Bayesian approach to…
Solving partial differential equations (PDEs) is the canonical approach for understanding the behavior of physical systems. However, large scale solutions of PDEs using state of the art discretization techniques remains an expensive…