Related papers: Physics-informed regularization and structure pres…

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…

While machine learning can accurately model process systems, models for decision making should also be structurally simple and physically interpretable. In process control, for example, (nearly) linear models are favored than nonlinear…

In various scientific and engineering applications, there is typically an approximate model of the underlying complex system, even though it contains both aleatoric and epistemic uncertainties. In this paper, we present a principled method…

In this work, we study model-based reinforcement learning (RL) in unknown stabilizable linear dynamical systems. When learning a dynamical system, one needs to stabilize the unknown dynamics in order to avoid system blow-ups. We propose an…

In this chapter we provide a theoretically founded investigation of state-of-the-art learning approaches for inverse problems from the point of view of spectral reconstruction operators. We give an extended definition of regularization…

Reinforcement Learning (RL) of robotic manipulation skills, despite its impressive successes, stands to benefit from incorporating domain knowledge from control theory. One of the most important properties that is of interest is control…

Quantum fields are generally taken to be operator-valued distributions, linear functionals of test functions into an algebra of operators; here the effective dynamics of an interacting quantum field is taken to be nonlinearly modified by…

Hamiltonian Operator Inference has been introduced in [Sharma, H., Wang, Z., Kramer, B., Physica D: Nonlinear Phenomena, 431, p.133122, 2022] to learn structure-preserving reduced-order models (ROMs) for Hamiltonian systems. This approach…

In order to tackle the difficulty associated with the ill-posed nature of the image registration problem, regularization is often used to constrain the solution space. For most learning-based registration approaches, the regularization…

The present paper deals with the data-driven design of regularizers in the form of artificial neural networks, for solving certain inverse problems formulated as optimal control problems. These regularizers aim at improving accuracy,…

The combination of deep neural nets and theory-driven models, which we call deep grey-box modeling, can be inherently interpretable to some extent thanks to the theory backbone. Deep grey-box models are usually learned with a regularized…

Physics-Informed Neural Networks (PINNs) have recently shown great promise as a way of incorporating physics-based domain knowledge, including fundamental governing equations, into neural network models for many complex engineering systems.…

Learning kinetic systems from data is one of the core challenges in many fields. Identifying stable models is essential for the generalization capabilities of data-driven inference. We introduce a computationally efficient framework, called…

Regularization is a central tool for addressing ill-posedness in inverse problems and statistical estimation, with the choice of a suitable penalty often determining the reliability and interpretability of downstream solutions. While recent…

Learning effective regularization is crucial for solving ill-posed inverse problems, which arise in a wide range of scientific and engineering applications. While data-driven methods that parameterize regularizers using deep neural networks…

Given (small amounts of) time-series' data from a high-dimensional, fine-grained, multiscale dynamical system, we propose a generative framework for learning an effective, lower-dimensional, coarse-grained dynamical model that is predictive…

Dealing with high variance is a significant challenge in model-free reinforcement learning (RL). Existing methods are unreliable, exhibiting high variance in performance from run to run using different initializations/seeds. Focusing on…

Here we present an expository, general analysis of valid post-selection or post-regularization inference about a low-dimensional target parameter, $\alpha$, in the presence of a very high-dimensional nuisance parameter, $\eta$, which is…

Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…

Solving inverse problems involving measurement noise and modeling errors requires regularization in order to avoid data overfit. Geophysical inverse problems, in which the Earth's highly heterogeneous structure is unknown, present a…