Related papers: Building symmetries into data-driven manifold dyna…
Identifying the intrinsic coordinates or modes of the dynamical systems is essential to understand, analyze, and characterize the underlying dynamical behaviors of complex systems. For nonlinear dynamical systems, this presents a critical…
This work presents the application of a recently developed parametric, non-intrusive, and multi-fidelity reduced-order modeling method on high-dimensional displacement and stress fields arising from the structural analysis of geometries…
Leveraging the intrinsic symmetries in data for clear and efficient analysis is an important theme in signal processing and other data-driven sciences. A basic example of this is the ubiquity of the discrete Fourier transform which arises…
High-dimensional big data appears in many research fields such as image recognition, biology and collaborative filtering. Often, the exploration of such data by classic algorithms is encountered with difficulties due to `curse of…
We are interested in derivative-free optimization of high-dimensional functions. The sample complexity of existing methods is high and depends on problem dimensionality, unlike the dimensionality-independent rates of first-order methods.…
Normalizing flows are generative models that provide tractable density estimation via an invertible transformation from a simple base distribution to a complex target distribution. However, this technique cannot directly model data…
Chaotic systems are notoriously challenging to predict because of their sensitivity to perturbations and errors due to time stepping. Despite this unpredictable behavior, for many dissipative systems the statistics of the long term…
In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on…
Starting from limited measurements of a turbulent flow, data assimilation (DA) attempts to estimate all the spatio-temporal scales of motion. Success is dependent on whether the system is observable from the measurements, or how much of the…
The theory of slow manifolds is an important tool in the study of deterministic dynamical systems, giving a practical method by which to reduce the number of relevant degrees of freedom in a model, thereby often resulting in a considerable…
Flow-based Generative Models (FGMs) effectively transform noise into complex data distributions. Incorporating Optimal Transport (OT) to couple noise and data during FGM training has been shown to improve the straightness of flow…
This paper presents a data-integrated framework for learning the dynamics of fractional-order nonlinear systems in both discrete-time and continuous-time settings. The proposed framework consists of two main steps. In the first step,…
We develop a deep learning methodology for the simultaneous discovery of multiple nontrivial continuous symmetries across an entire labelled dataset. The symmetry transformations and the corresponding generators are modeled with fully…
This work introduces a method for learning low-dimensional models from data of high-dimensional black-box dynamical systems. The novelty is that the learned models are exactly the reduced models that are traditionally constructed with model…
It is challenging to perform system identification on soft robots due to their underactuated, high-dimensional dynamics. In this work, we present a data-driven modeling framework, based on geometric mechanics (also known as gauge theory)…
Embedding graphs in continous spaces is a key factor in designing and developing algorithms for automatic information extraction to be applied in diverse tasks (e.g., learning, inferring, predicting). The reliability of graph embeddings…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
Manifold learning based methods have been widely used for non-linear dimensionality reduction (NLDR). However, in many practical settings, the need to process streaming data is a challenge for such methods, owing to the high computational…
Manifold models provide low-dimensional representations that are useful for processing and analyzing data in a transformation-invariant way. In this paper, we study the problem of learning smooth pattern transformation manifolds from image…
Flow models are a cornerstone of modern machine learning. They are generative models that progressively transform probability distributions according to learned dynamics. Specifically, they learn a continuous-time Markov process that…