Related papers: Finding the Underlying Viscoelastic Constitutive E…
In this paper, we study the numerical algorithm for a nonlinear poroelasticity model with nonlinear stress-strain relations. By using variable substitution, the original problem can be reformulated to a new coupled fluid-fluid system, that…
In the theory of viscoelasticity, an important class of models admits a representation in terms of springs and dashpots. Widely used members of this class are the Maxwell model and its extended version. This paper concerns resolvent…
Physics-based models often involve large systems of parametrized partial differential equations, where design parameters control various properties. However, high-fidelity simulations of such systems on large domains or with high grid…
Constitutive modeling lies at the core of mechanics, allowing us to map strains onto stresses for a material in a given mechanical setting. Historically, researchers relied on phenomenological modeling where simple mathematical…
The study presents a general framework for discovering underlying Partial Differential Equations (PDEs) using measured spatiotemporal data. The method, called Sparse Spatiotemporal System Discovery ($\text{S}^3\text{d}$), decides which…
We present a framework for fine-tuning flow-matching generative models to enforce physical constraints and solve inverse problems in scientific systems. Starting from a model trained on low-fidelity or observational data, we apply a…
Often the analysis of time-dependent chemical and biophysical systems produces high-dimensional time-series data for which it can be difficult to interpret which individual features are most salient. While recent work from our group and…
Machine learning techniques have been applied to enhance turbulence modeling in recent years. However, the "black box" nature of most machine learning techniques poses significant interpretability challenges in improving turbulence models.…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
The fully-implicit time discretization (i.e. the backward Euler formula) is applied to compressible nonlinear dynamical models of viscoelastic solids in the Eulerian description, i.e. in the actual deforming configuration. The Kelvin-Voigt…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
Discovering governing equations that describe complex chaotic systems remains a fundamental challenge in physics and neuroscience. Here, we introduce the PEM-UDE method, which combines the prediction-error method with universal differential…
Differential equations are important tools to portray dynamic problems, and are widely used in finance, engineering and biology. Here, multiple dynamic differential models were built innovatively, and discretized with the Runge-Kutta…
Lumped parameter methods aim to simplify the evolution of spatially-extended or continuous physical systems to that of a "lumped" element representative of the physical scales of the modeled system. For systems where the definition of a…
We propose in this work the first symmetric hyperbolic system of conservation laws to describe viscoelastic flows of Maxwell fluids, i.e. fluidswith memory that are characterized by one relaxation-time parameter. Precisely, the system of…
In this paper, we develop a novel contraction framework for stability analysis of discrete-time nonlinear systems with parameters following stochastic processes. For general stochastic processes, we first provide a sufficient condition for…
We study two closely related, nonlinear models of a viscoplastic solid. These models capture essential features of plasticity over a wide range of strain rates and applied stresses. They exhibit inelastic strain relaxation and steady flow…
In this work, we develop a method for learning interpretable, thermodynamically stable and Galilean invariant partial differential equations (PDEs) based on the Conservation-dissipation Formalism of irreversible thermodynamics. As governing…
Classically, the mechanical response of materials is described through constitutive models, often in the form of constrained ordinary differential equations. These models have a very limited number of parameters, yet, they are extremely…
Using mode-coupling theory, we derive a constitutive equation for the nonlinear rheology of dense colloidal suspensions under arbitrary time-dependent homogeneous flow. Generalizing previous results for simple shear, this allows the full…