Related papers: Deep Reinforcement Learning for Adaptive Mesh Refi…

The Deep Fourier Residual (DFR) method is a specific type of variational physics-informed neural networks (VPINNs). It provides a robust neural network-based solution to partial differential equations (PDEs). The DFR strategy is based on…

Learning models that are robust to distribution shifts is a key concern in the context of their real-life applicability. Invariant Risk Minimization (IRM) is a popular framework that aims to learn robust models from multiple environments.…

Many recent successful (deep) reinforcement learning algorithms make use of regularization, generally based on entropy or Kullback-Leibler divergence. We propose a general theory of regularized Markov Decision Processes that generalizes…

We analyze optimal complexity of adaptive finite element methods (AFEMs) for general second-order linear elliptic partial differential equations (PDEs) in the Lax-Milgram setting. To this end, we formulate an adaptive algorithm which steers…

We investigate the applicability of deep reinforcement learning algorithms to the adaptive initial access beam alignment problem for mmWave communications using the state-of-the-art proximal policy optimization algorithm as an example. In…

The use of neural networks to approximate partial differential equations (PDEs) has gained significant attention in recent years. However, the approximation of PDEs with localised phenomena, e.g., sharp gradients and singularities, remains…

We propose policy gradient algorithms for solving a risk-sensitive reinforcement learning (RL) problem in on-policy as well as off-policy settings. We consider episodic Markov decision processes, and model the risk using the broad class of…

Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remains challenging, often leading to limited accuracy and…

Bayesian approaches developed to solve the optimal design of sequential experiments are mathematically elegant but computationally challenging. Recently, techniques using amortization have been proposed to make these Bayesian approaches…

We consider goal-oriented adaptive space-time finite-element discretizations of the parabolic heat equation on completely unstructured simplicial space-time meshes. In some applications, we are interested in an accurate computation of some…

A deep reinforcement learning (DRL) agent observes its states through observations, which may contain natural measurement errors or adversarial noises. Since the observations deviate from the true states, they can mislead the agent into…

Adaptive meshing is a fundamental component of adaptive finite element methods. This includes refining and coarsening meshes locally. In this work, we are concerned with the red-green-blue refinement strategy in two dimensions and its…

Motivated by the emerging use of multi-agent reinforcement learning (MARL) in engineering applications such as networked robotics, swarming drones, and sensor networks, we investigate the policy evaluation problem in a fully decentralized…

Deep Reinforcement Learning (DRL) is a quickly evolving research field rooted in operations research and behavioural psychology, with potential applications extending across various domains, including robotics. This thesis delineates the…

Algebraic Multigrid (AMG) methods are state-of-the-art algebraic solvers for partial differential equations. Still, their efficiency depends heavily on the choice of suitable parameters and/or ingredients. Paradigmatic examples include the…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method 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…

Training nonlinear parametrizations such as deep neural networks to numerically approximate solutions of partial differential equations is often based on minimizing a loss that includes the residual, which is analytically available in…

We introduce a distributional method for learning the optimal policy in risk averse Markov decision process with finite state action spaces, latent costs, and stationary dynamics. We assume sequential observations of states, actions, and…

Ensuring reliability in modern software systems requires rigorous pre-production testing across highly heterogeneous and evolving environments. Because exhaustive evaluation is infeasible, practitioners must decide how to allocate limited…