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Distributionally robust optimization (DRO) problems are increasingly seen as a viable method to train machine learning models for improved model generalization. These min-max formulations, however, are more difficult to solve. We therefore…
We consider the problem of learning a graph from a finite set of noisy graph signal observations, the goal of which is to find a smooth representation of the graph signal. Such a problem is motivated by the desire to infer relational…
Spatially referenced datasets have become increasingly prevalent across many fields, largely driven by advances in data collection methods such as satellite remote sensing. In many applications, predictions at unobserved locations are…
Nonlinear dynamics are ubiquitous in science and engineering applications, but the physics of most complex systems is far from being fully understood. Discovering interpretable governing equations from measurement data can help us…
We propose a high-order stochastic-statistical moment closure model for efficient ensemble prediction of leading-order statistical moments and probability density functions in multiscale complex turbulent systems. The statistical moment…
Sliding mode control (SMC) is a robust and computationally efficient solution for tracking control problems of highly nonlinear systems with a great deal of uncertainty. High frequency oscillations due to chattering phenomena and…
Reservoir Computing (RC), a type of recurrent random neural network, is a powerful framework for modeling complex and chaotic dynamics. However, its autonomous (closed-loop) operation is often plagued by inherent instability. Moreover,…
Stochastic dynamical systems have emerged as fundamental models across numerous application domains, providing powerful mathematical representations for capturing uncertain system behavior. In this paper, we address the problem of runtime…
Stochastic and (distributionally) robust optimization problems often become computationally challenging as the number of scenarios or data points increases. Scenario reduction is therefore a key technique for improving tractability. We…
There is growing interest in reinforcement learning (RL) methods that leverage the simulator's derivatives to improve learning efficiency. While early gradient-based approaches have demonstrated superior performance compared to…
This paper extends the deterministic Lyapunov-based stabilization framework to random hyperbolic systems of conservation laws, where uncertainties arise in boundary controls and initial data. Building on the finite volume discretization…
Recently it has been reported that biased range-measurements among neighboring agents in the gradient distance-based formation control can lead to predictable collective motion. In this paper we take advantage of this effect and by…
We derive and prove the `fast response' formula for the linear response, the parameter derivatives of long-time-averaged statistics, of hyperbolic deterministic chaotic systems. The expression is pointwisely defined so we can compute the…
This paper considers a class of constrained stochastic composite optimization problems whose objective function is given by the summation of a differentiable (possibly nonconvex) component, together with a certain non-differentiable (but…
Stochastic model predictive control (SMPC) has been a promising solution to complex control problems under uncertain disturbances. However, traditional SMPC approaches either require exact knowledge of probabilistic distributions, or rely…
We introduce a novel adaptive damping technique for an inertial gradient system which finds application as a gradient descent algorithm for unconstrained optimisation. In an example using the non-convex Rosenbrock's function, we show an…
Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of…
Molecular motors and other complex nonequilibrium systems are controlled by large sets of design parameters, and optimizing those parameters requires computing sensitivities -- derivatives of dynamical observables with respect to the…
We investigate Weierstrass functions with roughness parameter $\gamma$ that are H\"older continuous with coefficient $H={\log\gamma}/{\log \frac12}.$ Analytical access is provided by an embedding into a dynamical system related to the baker…
Persistence diagrams play a fundamental role in Topological Data Analysis where they are used as topological descriptors of filtrations built on top of data. They consist in discrete multisets of points in the plane $\mathbb{R}^2$ that can…