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Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PDEs is often a challenging task. Inspired by the traditional…
We present a meshfree numerical solver for scalar conservation laws in one space dimension. Points representing the solution are moved according to their characteristic velocities. Particle interaction is resolved by purely local particle…
Deep reinforcement learning has gathered much attention recently. Impressive results were achieved in activities as diverse as autonomous driving, game playing, molecular recombination, and robotics. In all these fields, computer programs…
Learning deep representations to solve complex machine learning tasks has become the prominent trend in the past few years. Indeed, Deep Neural Networks are now the golden standard in domains as various as computer vision, natural language…
Running high-resolution physical models is computationally expensive and essential for many disciplines. Agriculture, transportation, and energy are sectors that depend on high-resolution weather models, which typically consume many hours…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
We introduce a novel class of algorithms to efficiently approximate the unknown return distributions in policy evaluation problems from distributional reinforcement learning (DRL). The proposed distributional dynamic programming algorithms…
Multiscale dynamical systems, modeled by high-dimensional stiff ordinary differential equations (ODEs) with wide-ranging characteristic timescales, arise across diverse fields of science and engineering, but their numerical solvers often…
Network slicing-based communication systems can dynamically and efficiently allocate resources for diversified services. However, due to the limitation of the network interface on channel access and the complexity of the resource…
Deep learning has provided new ways of manipulating, processing and analyzing data. It sometimes may achieve results comparable to, or surpassing human expert performance, and has become a source of inspiration in the era of artificial…
Neural networks can approximate solutions to partial differential equations, but they often break the very laws they are meant to model-creating mass from nowhere, drifting shocks, or violating conservation and entropy. We address this by…
In this paper we shall introduce a simple, effective numerical method for finding differential operators for scalar and vector-valued functions on surfaces. The key idea of our algorithm is to develop an intrinsic and unified way to compute…
The field development optimization (FDO) problem represents a challenging mixed-integer nonlinear programming (MINLP) problem in which we seek to obtain the number of wells, their type, location, and drilling sequence that maximizes an…
State-of-the-art Mixed Integer Linear Program (MILP) solvers combine systematic tree search with a plethora of hard-coded heuristics, such as the branching rule. The idea of learning branching rules from data has received increasing…
Deep reinforcement learning (RL) has made it possible to solve complex robotics problems using neural networks as function approximators. However, the policies trained on stationary environments suffer in terms of generalization when…
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…
The popularity of deep reinforcement learning (DRL) methods in economics have been exponentially increased. DRL through a wide range of capabilities from reinforcement learning (RL) and deep learning (DL) for handling sophisticated dynamic…
We consider the challenge of policy simplification and verification in the context of policies learned through reinforcement learning (RL) in continuous environments. In well-behaved settings, RL algorithms have convergence guarantees in…
We consider the joint design and control of discrete-time stochastic dynamical systems over a finite time horizon. We formulate the problem as a multi-step optimization problem under uncertainty seeking to identify a system design and a…
Deep reinforcement learning has shown remarkable success in the past few years. Highly complex sequential decision making problems have been solved in tasks such as game playing and robotics. Unfortunately, the sample complexity of most…