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Scientific machine learning is an emerging field that broadly describes the combination of scientific computing and machine learning to address challenges in science and engineering. Within the context of differential equations, this has…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

Differential equations are frequently used in engineering domains, such as modeling and control of industrial systems, where safety and performance guarantees are of paramount importance. Traditional physics-based modeling approaches…

We present a method for learning to satisfy uncertain constraints from demonstrations. Our method uses robust optimization to obtain a belief over the potentially infinite set of possible constraints consistent with the demonstrations, and…

We propose a framework for robust and efficient training of Dense Object Nets (DON) with a focus on multi-object robot manipulation scenarios. DON is a popular approach to obtain dense, view-invariant object descriptors, which can be used…

Neural ordinary differential equations (Neural ODEs) are an effective framework for learning dynamical systems from irregularly sampled time series data. These models provide a continuous-time latent representation of the underlying…

We propose a data-driven framework for learning reduced-order moment dynamics from PDE-governed systems using Neural ODEs. In contrast to derivative-based methods like SINDy, which necessitate densely sampled data and are sensitive to…

The operator learning has received significant attention in recent years, with the aim of learning a mapping between function spaces. Prior works have proposed deep neural networks (DNNs) for learning such a mapping, enabling the learning…

Analyzing nonlinear systems with attracting robust invariant sets (RISs) requires estimating their domains of attraction (DOAs). Despite extensive research, accurately characterizing DOAs for general nonlinear systems remains challenging…

Active localization is the problem of generating robot actions that allow it to maximally disambiguate its pose within a reference map. Traditional approaches to this use an information-theoretic criterion for action selection and…

Mastering complex sequential tasks continues to pose a significant challenge in robotics. While there has been progress in learning long-horizon manipulation tasks, most existing approaches lack rigorous mathematical guarantees for ensuring…

Neural ordinary differential equations (ODEs) have attracted much attention as continuous-time counterparts of deep residual neural networks (NNs), and numerous extensions for recurrent NNs have been proposed. Since the 1980s, ODEs have…

This paper presents a novel motion and trajectory planning algorithm for nonholonomic mobile robots that uses recent advances in deep reinforcement learning. Starting from a random initial state, i.e., position, velocity and orientation,…

The process of training an artificial neural network involves iteratively adapting its parameters so as to minimize the error of the network's prediction, when confronted with a learning task. This iterative change can be naturally…

Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…

We present a framework and algorithms to learn controlled dynamics models using neural stochastic differential equations (SDEs) -- SDEs whose drift and diffusion terms are both parametrized by neural networks. We construct the drift term to…

Motion planning is a mature area of research in robotics with many well-established methods based on optimization or sampling the state space, suitable for solving kinematic motion planning. However, when dynamic motions under constraints…

Precise trajectory tracking for legged robots can be challenging due to their high degrees of freedom, unmodeled nonlinear dynamics, or random disturbances from the environment. A commonly adopted solution to overcome these challenges is to…

In this chapter, we utilize dynamical systems to analyze several aspects of machine learning algorithms. As an expository contribution we demonstrate how to re-formulate a wide variety of challenges from deep neural networks, (stochastic)…

As autonomous systems become more complex and integral in our society, the need to accurately model and safely control these systems has increased significantly. In the past decade, there has been tremendous success in using deep learning…