Related papers: Evaluating PDE discovery methods for multiscale mo…
Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…
Machine learning for scientific applications faces the challenge of limited data. We propose a framework that leverages a priori known physics to reduce overfitting when training on relatively small datasets. A deep neural network is…
Data-driven discovery of dynamics in biological systems allows for better observation and characterization of processes, such as calcium signaling in cell culture. Recent advancements in techniques allow the exploration of previously…
We propose a two-stage method called \textit{Spline Assisted Partial Differential Equation based Model Identification (SAPDEMI)} to identify partial differential equation (PDE)-based models from noisy data. In the first stage, we employ the…
The viscosity and self-diffusion constant of particle-based mesoscale hydrodynamic methods, multi-particle collision dynamics (MPC) and dissipative particle dynamics (DPD), are investigated, both with and without angular-momentum…
Causal discovery algorithms based on probabilistic graphical models have emerged in geoscience applications for the identification and visualization of dynamical processes. The key idea is to learn the structure of a graphical model from…
Parameter estimation for non-stationary stochastic differential equations (SDE) with an arbitrary nonlinear drift, and nonlinear diffusion is accomplished in combination with a non-parametric clustering methodology. Such a model-based…
Probability Density Estimation (PDE) is a multivariate discrimination technique based on sampling signal and background densities defined by event samples from data or Monte-Carlo (MC) simulations in a multi-dimensional phase space. In this…
Calcium is an ubiquitous second messenger that triggers a plethora of key physiological responses. The events are initiated in micro- or nano-sized compartments and determined by the complex interactions with calcium-binding proteins and…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
Partial differential equations (PDEs) are widely used for the description of physical and engineering phenomena. Some key parameters involved in PDEs, which represent certain physical properties with important scientific interpretations,…
Spatially dependent parameters of a two-component chaotic reaction-diffusion PDE model describing ocean ecology are observed by sampling a single species. We estimate model parameters and the other species in the system by…
The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in…
Recent advances in deep learning have inspired numerous works on data-driven solutions to partial differential equation (PDE) problems. These neural PDE solvers can often be much faster than their numerical counterparts; however, each…
Transport-dominated partial differential equation models have been used extensively over the past two decades to describe various collective migration phenomena in cell biology and ecology. To understand the behaviour of these models (and…
This paper presents a novel data-driven approach to identify partial differential equation (PDE) parameters of a dynamical system. Specifically, we adopt a mathematical "transport" model for the solution of the dynamical system at specific…
Computation of biological processes creates great promise for everyday life and great challenges for physical scientists. Simulations of molecular dynamics appeal to biologists as a natural extension of structural biology. Once biologists…
There have been recent efforts that combine seemingly disparate methods, extremum seeking (ES) optimization and partial differential equation (PDE) backstepping, to address the problem of model-free optimization with PDE actuator dynamics.…
Scientific machine learning has been successfully applied to inverse problems and PDE discovery in computational physics. One caveat concerning current methods is the need for large amounts of ("clean") data, in order to characterize the…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…