Related papers: A Bayesian framework for discovering interpretable…

The dynamics of biological systems, from proteins to cells to organisms, is complex and stochastic. To decipher their physical laws, we need to bridge between experimental observations and theoretical modeling. Thanks to progress in…

We introduce a physics-informed neural framework for modeling static and time-dependent galactic gravitational potentials. The method combines data-driven learning with embedded physical constraints to capture complex, small-scale features…

Modeling complex spatiotemporal dynamics, particularly in far-from-equilibrium systems, remains a grand challenge in science. The governing partial differential equations (PDEs) for these systems are often intractable to derive from first…

This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…

We develop a novel data-driven approach to the inverse problem of classical statistical mechanics: given experimental data on the collective motion of a classical many-body system, how does one characterise the free energy landscape of that…

Accurate models of the world are built upon notions of its underlying symmetries. In physics, these symmetries correspond to conservation laws, such as for energy and momentum. Yet even though neural network models see increasing use in the…

In this paper we extend the work of Smith and Papamichail (1999) and present fast approximate Bayesian algorithms for learning in complex scenarios where at any time frame, the relationships between explanatory state space variables can be…

We introduce an evidence-driven Bayesian formulation of physics-informed neural networks that enables automatic optimization of loss weights between PDE residuals, boundary conditions, and observational data. Unlike existing Bayesian PINN…

The existence or not of pathologies in the context of Lagrangian theory is studied with the aid of Machine Learning algorithms. Using an example in the framework of classical mechanics, we make a proof of concept, that the construction of…

Realistic models of physical world rely on differentiable symmetries that, in turn, correspond to conservation laws. Recent works on Lagrangian and Hamiltonian neural networks show that the underlying symmetries of a system can be easily…

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…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Identifying accurate dynamic models is required for the simulation and control of various technical systems. In many important real-world applications, however, the two main modeling approaches often fail to meet requirements: first…

Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a…

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…

Unveiling the underlying governing equations of nonlinear dynamic systems remains a significant challenge. Insufficient prior knowledge hinders the determination of an accurate candidate library, while noisy observations lead to imprecise…

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…

An activity fundamental to science is building mathematical models. These models are used to both predict the results of future experiments and gain insight into the structure of the system under study. We present an algorithm that…

While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…

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…