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Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural…
A large class of inverse problems for PDEs are only well-defined as mappings from operators to functions. Existing operator learning frameworks map functions to functions and need to be modified to learn inverse maps from data. We propose a…
Machine learning, especially deep learning is gaining much attention due to the breakthrough performance in various cognitive applications. Recently, neural networks (NN) have been intensively explored to model partial differential…
Adapter-Tuning (AT) method involves freezing a pre-trained model and introducing trainable adapter modules to acquire downstream knowledge, thereby calibrating the model for better adaptation to downstream tasks. This paper proposes a…
Design and optimal control problems are among the fundamental, ubiquitous tasks we face in science and engineering. In both cases, we aim to represent and optimize an unknown (black-box) function that associates a performance/outcome to a…
Learning and solving governing equations of a physical system, represented by partial differential equations (PDEs), from data is a central challenge in a variety of areas of science and engineering. Traditional numerical methods for…
Network topology has significant impacts on operational performance of power systems. While extensive research efforts have been devoted to optimization of network topology for improving various system performances, the problem of how to…
Deep learning has been extensively employed as a powerful function approximator for modeling physics-based problems described by partial differential equations (PDEs). Despite their popularity, standard deep learning models often demand…
Recent Transformer-based methods have achieved advanced performance in point cloud registration by utilizing advantages of the Transformer in order-invariance and modeling dependency to aggregate information. However, they still suffer from…
Neural operators have achieved promising performance on partial differential equations (PDEs), but most existing models are built on fixed Eulerian coordinates. This mismatch between evolving physical structures and static coordinates…
Interface problems pose significant challenges due to the discontinuity of their solutions, particularly when they involve singular perturbations or high-contrast coefficients, resulting in intricate singularities that complicate…
Solutions of partial differential equations (PDEs) on manifolds have provided important applications in different fields in science and engineering. Existing methods are majorly based on discretization of manifolds as implicit functions,…
Covariate adjustment is a ubiquitous method used to estimate the average treatment effect (ATE) from observational data. Assuming a known graphical structure of the data generating model, recent results give graphical criteria for optimal…
In this paper, we propose a data-driven model reduction method to solve parabolic inverse source problems efficiently. Our method consists of offline and online stages. In the off-line stage, we explore the low-dimensional structures in the…
We propose a new neural network based method for solving inverse problems for partial differential equations (PDEs) by formulating the PDE inverse problem as a bilevel optimization problem. At the upper level, we minimize the data loss with…
Transformers have shown superior performance on various computer vision tasks with their capabilities to capture long-range dependencies. Despite the success, it is challenging to directly apply Transformers on point clouds due to their…
Partial Differential Equations (PDEs) with high dimensionality are commonly encountered in computational physics and engineering. However, finding solutions for these PDEs can be computationally expensive, making model-order reduction…
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…
Operator learning has become a powerful tool for accelerating the solution of parameterized partial differential equations (PDEs), enabling rapid prediction of full spatiotemporal fields for new initial conditions or forcing functions.…
Surrogate models are critical for accelerating computationally expensive simulations in science and engineering, particularly for solving parametric partial differential equations (PDEs). Developing practical surrogate models poses…