Related papers: Building symmetries into data-driven manifold dyna…
We introduce Coupled Flow Matching (CPFM), a framework that integrates controllable dimensionality reduction and high-fidelity reconstruction. CPFM learns coupled continuous flows for both the high-dimensional data x and the low-dimensional…
In our previous paper [N. Tsutsumi, K. Nakai and Y. Saiki, Chaos 32, 091101 (2022)], we proposed a method for constructing a system of differential equations of chaotic behavior from only observable deterministic time series, which we call…
Knowing the sea surface velocity field is essential for various applications, such as search and rescue operations and oil spill monitoring, where understanding the movement of objects or substances is critical. However, obtaining an…
Matching objectives underpin the success of modern generative models and rely on constructing conditional paths that transform a source distribution into a target distribution. Despite being a fundamental building block, conditional paths…
We show how the recent extension of spectral submanifold (SSM) theory to delay differential equations (DDEs) enables data-driven model reduction of nonlinear delay systems. First, using a scalar DDE with a single discrete delay, we compare…
Model reduction for fluid flow simulation continues to be of great interest across a number of scientific and engineering fields. In a previous work [arXiv:2104.13962], we explored the use of Neural Ordinary Differential Equations (NODE) as…
In contexts where data samples represent a physically stable state, it is often assumed that the data points represent the local minima of an energy landscape. In control theory, it is well-known that energy can serve as an effective…
Data-Driven Computational Mechanics is a novel computing paradigm that enables the transition from standard data-starved approaches to modern data-rich approaches. At this early stage of development, one can distinguish two mainstream…
We present a publicly accessible database designed to aid in the conception, training, demonstration, evaluation, and comparison of reduced-complexity models for fluid mechanics. Availability of high-quality flow data is essential for all…
Fundamental diagrams describe the relationship between speed, flow, and density for some roadway (or set of roadway) configuration(s). These diagrams typically do not reflect, however, information on how speed-flow relationships change as a…
We develop a reduced-order framework for optimizing mixing in two-dimensional incompressible flows. Instead of optimizing the full transport PDE, the method maximizes the length of advected material interfaces, leading to a…
Nowadays, interest in combining mathematical knowledge about phenomena and data from the physical system is growing. Past research was devoted to developing so-called high-fidelity models, intending to make them able to catch most of the…
Nudging is an important data assimilation technique where partial field measurements are used to control the evolution of a dynamical system and/or to reconstruct the entire phase-space configuration of the supplied flow. Here, we apply it…
Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…
We introduce a new heterogeneous multi-scale method for the simulation of flows of non-Newtonian fluids in general geometries and present its application to paradigmatic two-dimensional flows of polymeric fluids. Our method combines…
Finding a transformation between two unknown probability distributions from finite samples is crucial for modeling complex data distributions and performing tasks such as sample generation, domain adaptation and statistical inference. One…
The quest for simplification in physics drives the exploration of concise mathematical representations for complex systems. This Dissertation focuses on the concept of dimensionality reduction as a means to obtain low-dimensional…
Model order reduction provides low-complexity high-fidelity surrogate models that allow rapid and accurate solutions of parametric differential equations. The development of reduced order models for parametric \emph{nonlinear} Hamiltonian…
We develop a data-driven framework for learning and correcting non-autonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need…
We present a new turbulent data reconstruction method with supervised machine learning techniques inspired by super resolution and inbetweening, which can recover high-resolution turbulent flows from grossly coarse flow data in space and…