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We present a new multiphase-field theory for describing pattern formation in multi-domain and/or multi-component systems. The construction of the free energy functional and the dynamic equations is based on criteria that ensure mathematical…
The behavior of complex systems is determined not only by the topological organization of their interconnections but also by the dynamical processes taking place among their constituents. A faithful modeling of the dynamics is essential…
The calibration of solid constitutive models with full-field experimental data is a long-standing challenge, especially in materials which undergo large deformation. In this paper, we propose a physics-informed deep-learning framework for…
With the growing size and complexity of turbulent flow models, data compression approaches are of the utmost importance to analyze, visualize, or restart the simulations. Recently, in-situ autoencoder-based compression approaches have been…
The original models of causal dynamical triangulations construct space-time by arranging a set of simplices in layers separated by a fixed time-like distance. The importance of the foliation structure in the 2+1 dimensional model is studied…
System identification of complex and nonlinear systems is a central problem for model predictive control and model-based reinforcement learning. Despite their complexity, such systems can often be approximated well by a set of linear…
In this paper we continue the work of Kalnins et al in classifying all second-order conformally-superintegrable (Laplace-type) systems over conformally flat spaces, using tools from algebraic geometry and classical invariant theory. The…
Resolvent analysis identifies the most responsive forcings and most receptive states of a dynamical system, in an input--output sense, based on its governing equations. Interest in the method has continued to grow during the past decade due…
Calibrating simulation models that take large quantities of multi-dimensional data as input is a hard simulation optimization problem. Existing adaptive sampling strategies offer a methodological solution. However, they may not sufficiently…
We propose a multiscale approach for predicting quantities in dynamical systems which is explicitly structured to extract information in both fine-to-coarse and coarse-to-fine directions. We envision this method being generally applicable…
The identification of slow invariant manifolds (SIMs) is an essential part in model-order reduction for reactive systems. The mathematical definition of the SIM by Fenichel can be considered unsatisfactory, because it is only applicable to…
This paper introduces a novel method for approximating the dynamics of a large autonomous system projected onto a fixed subspace. The core contribution is a novel recursive algorithm to construct an effective time-dependent generator that…
Fault tree analysis is a well-known technique in reliability engineering and risk assessment, which supports decision-making processes and the management of complex systems. Traditionally, fault tree (FT) models are built manually together…
We show that, for a certain class of scaling matrices including the commonly used inverse square-root of the conditional Fisher Information, score-driven factor models are identifiable up to a multiplicative scalar constant under very mild…
In this paper, we investigate dynamic feature selection within multivariate time-series scenario, a common occurrence in clinical prediction monitoring where each feature corresponds to a bio-test result. Many existing feature selection…
This study presents the extension of the data-driven optimal prediction approach to the dynamical system with control. The optimal prediction is used to analyze dynamical systems in which the states consist of resolved and unresolved…
In the paper, effective filtering for a type of slow-fast data assimilation systems in Hilbert spaces is considered. Firstly, the system is reduced to a system on a random invariant manifold. Secondly, nonlinear filtering of the origin…
Dynamic mode decomposition (DMD) provides a principled approach to extract physically interpretable spatial modes from time-resolved flow field data, along with a linear model for how the amplitudes of these modes evolve in time. Recently,…
Invariant inference algorithms such as interpolation-based inference and IC3/PDR show that it is feasible, in practice, to find inductive invariants for many interesting systems, but non-trivial upper bounds on the computational complexity…
The objective of this paper is to design novel multi-layer neural network architectures for multiscale simulations of flows taking into account the observed data and physical modeling concepts. Our approaches use deep learning concepts…