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Interferometric closure invariants encode calibration-independent details of an object's morphology. Excepting simple cases, a direct backward transformation from closure invariants to morphologies is not well established. We demonstrate…

In this paper, we investigate tensor based nonintrusive reduced-order models (ROMs) for parametric cross-diffusion equations. The full-order model (FOM) consists of ordinary differential equations (ODEs) in matrix or tensor form resulting…

Designing learning systems which are invariant to certain data transformations is critical in machine learning. Practitioners can typically enforce a desired invariance on the trained model through the choice of a network architecture, e.g.…

Decision trees and systems of decision rules are widely used as classifiers, as a means for knowledge representation, and as algorithms. They are among the most interpretable models for data analysis. The study of the relationships between…

The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. A central challenge in this setting is backpropagation through the solution of an…

This work presents an approach to the inverse design of scattering systems by modifying the transmission matrix using reinforcement learning. We utilize Proximal Policy Optimization to navigate the highly non-convex landscape of the object…

Computational fluid dynamics (CFD) simulations play an important role in engineering science and applications, however, it is not applicable for problems requiring a large number of repeated calculations. Accordingly, many reduced-order…

Distributed optimization is fundamental to modern machine learning applications like federated learning, but existing methods often struggle with ill-conditioned problems and face stability-versus-speed tradeoffs. We introduce fractional…

Dynamical systems models such as recurrent neural networks (RNNs) are increasingly popular in theoretical neuroscience for hypothesis-generation and data analysis. Evaluating the dynamics in such models is key to understanding their learned…

Mobility on Demand (MoD) refers to mobility systems that operate on the basis of immediate travel demand. Typically, such a system consists of a fleet of vehicles that can be booked by customers when needed. The operation of these services…

We present a numerical methodology for construction of reduced order models, ROMs, of fluid flows through the combination of flow modal decomposition and regression analysis. Spectral proper orthogonal decomposition, SPOD, is applied to…

Building invariance to non-meaningful transformations is essential to building efficient and generalizable machine learning models. In practice, the most common way to learn invariance is through data augmentation. There has been recent…

In the context of simulation-based methods, multiple challenges arise, two of which are considered in this work. As a first challenge, problems including time-dependent phenomena with complex domain deformations, potentially even with…

This work is concerned with the dynamics of a slow-fast stochastic evolutionary system quantified with a scale parameter. An invariant foliation decomposes the state space into geometric regions of different dynamical regimes, and thus…

Reinforcement learning has emerged as a promising methodology for training robot controllers. However, most results have been limited to simulation due to the need for a large number of samples and the lack of automated-yet-safe data…

Several algorithms are presented for the accurate computation of the leaves in the foliation of an ODE near a hyperbolic fixed point. They are variations of a contraction mapping method in [25] to compute inertial manifolds, which…

This paper presents a physics-informed machine learning (ML) framework to construct reduced-order models (ROMs) for reactive-transport quantities of interest (QoIs) based on high-fidelity numerical simulations. QoIs include species decay,…

In this paper, we consider the learning of a Reduced-Order Linear Parameter-Varying Model (ROLPVM) of a nonlinear dynamical system based on data. This is achieved by a two-step procedure. In the first step, we learn a projection to a lower…

The problem of identifying geometric structure in data is a cornerstone of (unsupervised) learning. As a result, Geometric Representation Learning has been widely applied across scientific and engineering domains. In this work, we…

Invariant manifolds facilitate the understanding of nonlinear stochastic dynamics. When an invariant manifold is represented approximately by a graph for example, the whole stochastic dynamical system may be reduced or restricted to this…