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How can we explain the predictions of a machine learning model? When the data is structured as a multivariate time series, this question induces additional difficulties such as the necessity for the explanation to embody the time dependency…
We implement a computer-assisted approach that, under appropriate conditions, allows the bifurcation analysis of the coarse dynamic behavior of microscopic simulators without requiring the explicit derivation of closed macroscopic equations…
The computation of correspondences between shapes is a principal task in shape analysis. To this end, methods based on partial differential equations (PDEs) have been established, encompassing e.g. the classic heat kernel signature as well…
This study evaluates data-driven models from a dynamical system perspective, such as unstable fixed points, periodic orbits, chaotic saddle, Lyapunov exponents, manifold structures, and statistical values. We find that these dynamical…
Dynamical systems describe the changes in processes that arise naturally from their underlying physical principles, such as the laws of motion or the conservation of mass, energy or momentum. These models facilitate a causal explanation for…
Data can be assumed to be continuous functions defined on an infinite-dimensional space for many phenomena. However, the infinite-dimensional data might be driven by a small number of latent variables. Hence, factor models are relevant for…
Modeling of dynamic processes in nuclear reactors is carried out, mainly, on the basis of the multigroup diffusion approximation for the neutron flux. The basic model includes a multidimensional set of coupled parabolic equations and…
This paper addresses the problem of multi-step time series forecasting for non-stationary signals that can present sudden changes. Current state-of-the-art deep learning forecasting methods, often trained with variants of the MSE, lack the…
Dynamic simulators are computational models governed by differential equations that evolve over time. They are essential for scientific and engineering applications but remain challenging to emulate because of the unpredictable behavior of…
While diffusion models can successfully generate data and make predictions, they are predominantly designed for static images. We propose an approach for efficiently training diffusion models for probabilistic spatiotemporal forecasting,…
Ordinary differential equation models have become a standard tool for the mechanistic description of biochemical processes. If parameters are inferred from experimental data, such mechanistic models can provide accurate predictions about…
In this short note, we discuss the basic approach to computational modeling of dynamical systems. If a dynamical system contains multiple time scales, ranging from very fast to slow, computational solution of the dynamical system can be…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
Living biological tissue is a complex system, constantly growing and changing in response to external and internal stimuli. These processes lead to remarkable and intricate changes in shape. Modeling and understanding both natural and…
The oscillations observed in many time series, particularly in biomedicine, exhibit morphological variations over time. These morphological variations are caused by intrinsic or extrinsic changes to the state of the generating system,…
Temporal modulation unlocks possibilities to dynamically control and modify the response of electromagnetic systems. Employing explicit dependencies of circuit or surface parameters on time enables the engineering of systems with…
Given a set of inelastic material models, a microstructure, a macroscopic structural geometry, and a set of boundary conditions, one can in principle always solve the governing equations to determine the system's mechanical response.…
Data-driven model identification strategies can be used to obtain phenomenological models that capture the temporal evolution of observable data. While it is usually straightforward to obtain such a model from time series data, for instance…
We present a novel technique for assessing the dynamics of multiphase fluid flow in the oil reservoir. We demonstrate an efficient workflow for handling the 3D reservoir simulation data in a way which is orders of magnitude faster than the…
We propose a 1D unsteady model for supersonic single-phase ejectors. The model treats an ejector as a pipe network with two inputs and one output and combines a 1D gas dynamics formulation in each `pipe' with a junction model for…