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The sparse identification of nonlinear dynamics (SINDy) has been established as an effective technique to produce interpretable models of dynamical systems from time-resolved state data via sparse regression. However, to model parameterized…
In a mathematical model of interacting biological organisms, where external interventions may alter behavior over time, traditional models that assume fixed parameters usually do not capture the evolving dynamics. In oncology, this is…
Several recent experiments in biology study systems composed of several interacting elements, for example neuron networks. Normally, measurements describe only the collective behavior of the system, even if in most cases we would like to…
We study the spatial patterns formed by a system of interacting particles where the mobility of any individual is determined by the population crowding at two different spatial scales. In this way we model the behavior of some biological…
In animal societies as well as in human crowds, many observed collective behaviours result from self-organized processes based on local interactions among individuals. However, models of crowd dynamics are still lacking a systematic…
The discovery of governing differential equations from data is an open frontier in machine learning. The sparse identification of nonlinear dynamics (SINDy) \citep{brunton_discovering_2016} framework enables data-driven discovery of…
Many dynamical systems exhibit oscillatory behavior that can be modeled with differential equations. Recently, these equations have increasingly been derived through data-driven methods, including the transparent technique known as Sparse…
Particle dynamics and multi-agent systems provide accurate dynamical models for studying and forecasting the behavior of complex interacting systems. They often take the form of a high-dimensional system of differential equations…
Data-driven discovery of model equations is a powerful approach for understanding the behavior of dynamical systems in many scientific fields. In particular, the ability to learn mathematical models from data would benefit systems biology,…
The sparse identification of nonlinear dynamics (SINDy) has been established as an effective method to learn interpretable models of dynamical systems from data. However, for high-dimensional slow-fast dynamical systems, the regression…
A significant challenge in many fields of science and engineering is making sense of time-dependent measurement data by recovering governing equations in the form of differential equations. We focus on finding parsimonious ordinary…
The control of complex dynamical systems remains a fundamental challenge in science and engineering, where strong nonlinearities, the presence of noise, and computational constraints often pose significant obstacles in traditional control…
Many dynamical systems of interest are nonlinear, with examples in turbulence, epidemiology, neuroscience, and finance, making them difficult to control using linear approaches. Model predictive control (MPC) is a powerful model-based…
Cellular regulatory dynamics is driven by large and intricate networks of interactions at the molecular scale, whose sheer size obfuscates understanding. In light of limited experimental data, many parameters of such dynamics are unknown,…
We propose a fast probabilistic framework for identifying differential equations governing the dynamics of observed data. We recast the SINDy method within a Bayesian framework and use Gaussian approximations for the prior and likelihood to…
Dynamical systems are typically governed by a set of linear/nonlinear differential equations. Distilling the analytical form of these equations from very limited data remains intractable in many disciplines such as physics, biology, climate…
We present our recent work on stochastic particle systems on complex networks. As a noninteracting system we first consider the diffusive motion of a random walker on heterogeneous complex networks. We find that the random walker is…
Governing equations are essential to the study of nonlinear dynamics, often enabling the prediction of previously unseen behaviors as well as the inclusion into control strategies. The discovery of governing equations from data thus has the…
One challenge of physics is to explain how collective properties arise from microscopic interactions. Indeed, interactions form the building blocks of almost all physical theories and are described by polynomial terms in the action. The…
Identifying governing equations in physical and biological systems from datasets remains a long-standing challenge across various scientific disciplines, providing mechanistic insights into complex system evolution. Common methods like…