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Spatiotemporal dynamics models are fundamental for various domains, from heat propagation in materials to oceanic and atmospheric flows. However, currently available neural network-based spatiotemporal modeling approaches fall short when…

Theoretical studies have shown that stochasticity can affect the dynamics of ecosystems in counter-intuitive ways. However, without knowing the equations governing the dynamics of populations or ecosystems, it is difficult to ascertain the…

Considering a gas of self-propelled particles with binary interactions, we derive the hydrodynamic equations governing the density and velocity fields from the microscopic dynamics, in the framework of the associated Boltzmann equation.…

A recently introduced particle-based model for fluid dynamics with continuous velocities is generalized to model fluids with excluded volume effects. This is achieved through the use of biased stochastic multi-particle collisions which…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

Devising optimal interventions for constraining stochastic systems is a challenging endeavour that has to confront the interplay between randomness and nonlinearity. Existing methods for identifying the necessary dynamical adjustments…

Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…

We propose a probabilistic framework for developing computational models of biological neural systems. In this framework, physiological recordings are viewed as discrete-time partial observations of an underlying continuous-time stochastic…

Differential equations based on physical principals are used to represent complex dynamic systems in all fields of science and engineering. Through repeated use in both academics and industry, these equations have been shown to represent…

Self-propelled particles with hydrodynamic interactions (microswimmers) have previously been shown to produce long-range ordering phenomena. Many theoretical explanations for these collective phenomena are connected to instabilities in the…

A hybrid stochastic individual-based model of proliferating cells with chemotaxis is presented. The model is expressed by a branching diffusion process coupled to a partial differential equation describing concentration of a chemotactic…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

Many time series are effectively generated by a combination of deterministic continuous flows along with discrete jumps sparked by stochastic events. However, we usually do not have the equation of motion describing the flows, or how they…

We present a numerical method for learning unknown nonautonomous stochastic dynamical system, i.e., stochastic system subject to time dependent excitation or control signals. Our basic assumption is that the governing equations for the…

Inspired by dense contractile tissues, where cells are subject to periodic deformation, we formulate and study a generic hydrodynamic theory of pulsating active liquids. Combining mechanical and phenomenological arguments, we postulate that…

Extracting governing physical laws from computational or experimental data is crucial across various fields such as fluid dynamics and plasma physics. Many of those physical laws are dissipative due to fluid viscosity or plasma collisions.…

Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since…

Data-driven learning approaches for physics simulation, sometimes referred to as world models, have emerged as promising alternatives to traditional physics simulators due to their differentiable nature. Prior work has demonstrated…

We develop an approach to learn an interpretable semi-parametric model of a latent continuous-time stochastic dynamical system, assuming noisy high-dimensional outputs sampled at uneven times. The dynamics are described by a nonlinear…

Active nematics are a class of far-from-equilibrium materials characterized by local orientational order of force-generating, anisotropic constitutes. Traditional methods for predicting the dynamics of active nematics rely on hydrodynamic…