Related papers: Astral: training physics-informed neural networks …
We study the convergence of a class of gradient-based Model-Agnostic Meta-Learning (MAML) methods and characterize their overall complexity as well as their best achievable accuracy in terms of gradient norm for nonconvex loss functions. We…
This work focuses on developing methods for approximating the solution operators of a class of parametric partial differential equations via neural operators. Neural operators have several challenges, including the issue of generating…
The current work aims to incorporate physics-based loss in Physics Informed Neural Network (PINN) directly using the numerical residual obtained from the governing equation in any dicretized forward solver. PINN's major difficulties in…
Humans can naturally learn new and varying tasks in a sequential manner. Continual learning is a class of learning algorithms that updates its learned model as it sees new data (on potentially new tasks) in a sequence. A key challenge in…
Importance sampling has been successfully used to accelerate stochastic optimization in many convex problems. However, the lack of an efficient way to calculate the importance still hinders its application to Deep Learning. In this paper,…
In this work, we introduce a learning model designed to meet the needs of applications in which computational resources are limited, and robustness and interpretability are prioritized. Learning problems can be formulated as constrained…
Inverse reinforcement learning (IRL), which infers reward functions from demonstrations, is a valuable tool for modeling and understanding decision-making behavior. Many variants of IRL have been developed to capture complexities of human…
Teaching large language models (LLMs) to reason during post-training typically relies on reinforcement learning with explicit outcome- or process-based reward functions. However, in many real-world settings, obtaining or defining such…
This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…
Imitation learning is well-suited for robotic tasks where it is difficult to directly program the behavior or specify a cost for optimal control. In this work, we propose a method for learning the reward function (and the corresponding…
A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for…
Physics-Informed Machine Learning (PIML) has gained momentum in the last 5 years with scientists and researchers aiming to utilize the benefits afforded by advances in machine learning, particularly in deep learning. With large scientific…
In a general setting, we study a posteriori estimates used in finite element analysis to measure the error between a solution and its approximation. The latter is not necessarily generated by a finite element method. We show that the error…
Machine learning models are increasingly being utilized across various fields and tasks due to their outstanding performance and strong generalization capabilities. Nonetheless, their success hinges on the availability of large volumes of…
Physics-Informed Neural Networks (PINNs) embed the partial differential equations (PDEs) governing the system under study directly into the training of Neural Networks, ensuring solutions that respect physical laws. While effective for…
We introduce the Optimizing a Discrete Loss (ODIL) framework for the numerical solution of Partial Differential Equations (PDE) using machine learning tools. The framework formulates numerical methods as a minimization of discrete residuals…
This paper proposes a primal-dual framework to learn a stable estimator for linear constrained estimation problems leveraging the moving horizon approach. To avoid the online computational burden in most existing methods, we learn a…
This paper studies how to train machine-learning models that directly approximate the optimal solutions of constrained optimization problems. This is an empirical risk minimization under constraints, which is challenging as training must…
We present an architecture of a recurrent neural network (RNN) with a fully-connected deep neural network (DNN) as its feature extractor. The RNN is equipped with both causal temporal prediction and non-causal look-ahead, via…
In spite of the accomplishments of deep learning based algorithms in numerous applications and very broad corresponding research interest, at the moment there is still no rigorous understanding of the reasons why such algorithms produce…