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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…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…
We present a potent computational method for the solution of inverse problems in fluid mechanics. We consider inverse problems formulated in terms of a deterministic loss function that can accommodate data and regularization terms. We…
The optimal control of a mechanical system is of crucial importance in many realms. Typical examples are the determination of a time-minimal path in vehicle dynamics, a minimal energy trajectory in space mission design, or optimal motion…
We present a novel data- and first-principles-driven method for inferring the shape of a solid obstacle and its flow field in three-dimensional steady-state supersonic flows. The method combines the Optimizing a Discrete Loss (ODIL)…
Optimal power flow (OPF) is a critical optimization problem for power systems to operate at points where cost or other operational objectives are optimized. Due to the non-convexity of the set of feasible OPF operating points, it is…
We present theoretical and numerical results concerning the problem to find the path that minimizes the time to navigate between two given points in a complex fluid under realistic navigation constraints. We contrast deterministic Optimal…
Contactless manipulation of small objects is essential for biomedical and chemical applications, such as cell analysis, assisted fertilisation, and precision chemistry. Established methods, including optical, acoustic, and magnetic…
Efficient motion planning algorithms are of central importance for deploying robots in the real world. Unfortunately, these algorithms often drastically reduce the dimensionality of the problem for the sake of feasibility, thereby foregoing…
Multi-robot navigation and path planning in continuous state and action spaces with uncertain environments remains an open challenge. Deep Reinforcement Learning (RL) is one of the most popular paradigms for solving this task, but its…
Smart devices, storage and other distributed technologies have the potential to greatly improve the utilisation of network infrastructure and renewable generation. Decentralised control of these technologies overcomes many scalability and…
We present a flow-based approach to the optimal transport (OT) problem between two continuous distributions $\pi_0,\pi_1$ on $\mathbb{R}^d$, of minimizing a transport cost $\mathbb{E}[c(X_1-X_0)]$ in the set of couplings $(X_0,X_1)$ whose…
This paper addresses the problem of guidance and control of underwater vehicles. A multi-level control strategy is used to determine (1) outer-loop path-following commands and (2) inner-loop actuation commands. Specifically, a line-of-sight…
This research gauges the ability of deep reinforcement learning (DRL) techniques to assist the optimization and control of fluid mechanical systems. It combines a novel, "degenerate" version of the proximal policy optimization (PPO)…
Control theory provides engineers with a multitude of tools to design controllers that manipulate the closed-loop behavior and stability of dynamical systems. These methods rely heavily on insights about the mathematical model governing the…
Creating safe paths in unknown and uncertain environments is a challenging aspect of leader-follower formation control. In this architecture, the leader moves toward the target by taking optimal actions, and followers should also avoid…
The quest for the optimal navigation strategy in a complex environment is at the heart of microswimmer applications like cargo carriage or drug targeting to cancer cells. Here, we formulate a variational Fermat's principle for microswimmers…
Control of systems operating in unexplored environments is challenging due to lack of complete model knowledge. Additionally, under measurement noises, data collected from onboard sensors are of limited accuracy. This paper considers…
Gathering data and identifying events in various traffic situations remains an essential challenge for the systematic evaluation of a perception system's performance. Analyzing large-scale, typically unstructured, multi-modal, time series…
Optimal-Transport Distributionally Robust Optimization (OT-DRO) robustifies data-driven decision-making under uncertainty by capturing the sampling-induced statistical error via optimal transport ambiguity sets. The standard OT-DRO pipeline…