Related papers: Joint Parameter Discovery and Generative Modeling …
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…
Despite rapid progress in live-imaging techniques, many complex biophysical and biochemical systems remain only partially observable, thus posing the challenge to identify valid theoretical models and estimate their parameters from an…
The fundamental laws of physics are intrinsically geometric, dictating the evolution of systems through principles of symmetry and conservation. While modern machine learning offers powerful tools for modeling complex dynamics from data,…
Most common mechanistic models are traditionally presented in mathematical forms to explain a given physical phenomenon. Machine learning algorithms, on the other hand, provide a mechanism to map the input data to output without explicitly…
Obtaining system parameters and reconstructing the full flow state from limited velocity observations using conventional fluid dynamics solvers can be prohibitively expensive. Here we employ machine learning algorithms to overcome the…
We introduce a novel statistical framework for analyzing the GPS data of a single individual. Our approach models daily GPS observations as noisy measurements of an underlying random trajectory, enabling the definition of meaningful…
Neutrino oscillations encode fundamental information about neutrino masses and mixing parameters, offering a unique window into physics beyond the Standard Model. Estimating these parameters from oscillation probability maps is, however,…
A key ingredient to achieving intelligent behavior is physical understanding that equips robots with the ability to reason about the effects of their actions in a dynamic environment. Several methods have been proposed to learn dynamics…
We study the fundamental problem of learning a marginally stable unknown nonlinear dynamical system. We describe an algorithm for this problem, based on the technique of spectral filtering, which learns a mapping from past observations to…
Advancements in artificial intelligence call for a deeper understanding of the fundamental mechanisms underlying deep learning. In this work, we propose a theoretical framework to analyze learning dynamics through the lens of dynamical…
Motivated by recent progress in data assimilation, we develop an algorithm to dynamically learn the parameters of a chaotic system from partial observations. Under reasonable assumptions, we rigorously establish the convergence of this…
Nonlinear dynamical systems with regime transitions are typically described by ordinary differential equations with jumping parameters parameters. Traditional methods often treat change-point detection and parameter estimation as separate…
We present the interpretable meta neural ordinary differential equation (iMODE) method to rapidly learn generalizable (i.e., not parameter-specific) dynamics from trajectories of multiple dynamical systems that vary in their physical…
The kinematic properties of mechanisms are well known by the researchers and teachers. The theory based on the study of Jacobian matrices allows us to explain, for example, the singular configuration. However, in many cases, the physical…
Many collective systems exist in nature far from equilibrium, ranging from cellular sheets up to flocks of birds. These systems reflect a form of active matter, whereby individual material components have internal energy. Under specific…
The task of modelling and forecasting a dynamical system is one of the oldest problems, and it remains challenging. Broadly, this task has two subtasks - extracting the full dynamical information from a partial observation; and then…
Critical points separate distinct dynamical regimes of complex systems, often delimiting functional or macroscopic phases in which the system operates. However, the long-term prediction of critical regimes and behaviors is challenging given…
We consider a dynamic method, based on synchronization and adaptive control, to estimate unknown parameters of a nonlinear dynamical system from a given scalar chaotic time series. We present an important extension of the method when time…
This paper proposes a tractable framework to determine key characteristics of non-linear dynamic systems by converting physics-informed neural networks to a mixed integer linear program. Our focus is on power system applications.…
In todays age of data, discovering relationships between different variables is an interesting and a challenging problem. This problem becomes even more critical with regards to complex dynamical systems like weather forecasting and…