Related papers: Learning Stochastic Behaviour from Aggregate Data
McKean-Vlasov SDEs describe systems where the dynamics depend on the law of the process. The corresponding Fokker-Planck equation is a nonlinear, nonlocal PDE for the corresponding measure flow. In the presence of common noise and…
Identification of nonlinear dynamical systems is crucial across various fields, facilitating tasks such as control, prediction, optimization, and fault detection. Many applications require methods capable of handling complex systems while…
Many real-world systems, such as moving planets, can be considered as multi-agent dynamic systems, where objects interact with each other and co-evolve along with the time. Such dynamics is usually difficult to capture, and understanding…
We investigate methods for learning partial differential equation (PDE) models from spatiotemporal data under biologically realistic levels and forms of noise. Recent progress in learning PDEs from data have used sparse regression to select…
Inspired by the modeling of grain growth in polycrystalline materials, we consider a nonlinear Fokker-Plank model, with inhomogeneous diffusion and with variable mobility parameters. We develop large time asymptotic analysis of such…
Federated Learning(FL) is popular as a privacy-preserving machine learning paradigm for generating a single model on decentralized data. However, statistical heterogeneity poses a significant challenge for FL. As a subfield of FL,…
In this work, we propose a method to learn multivariate probability distributions using sample path data from stochastic differential equations. Specifically, we consider temporally evolving probability distributions (e.g., those produced…
We introduce Weak-PDE-LEARN, a Partial Differential Equation (PDE) discovery algorithm that can identify non-linear PDEs from noisy, limited measurements of their solutions. Weak-PDE-LEARN uses an adaptive loss function based on weak forms…
The Fokker-Planck equations for stochastic dynamical systems, with non-Gaussian $\alpha-$stable symmetric L\'evy motions, have a nonlocal or fractional Laplacian term. This nonlocality is the manifestation of the effect of non-Gaussian…
We develop a framework for learning sparse nonparametric directed acyclic graphs (DAGs) from data. Our approach is based on a recent algebraic characterization of DAGs that led to a fully continuous program for score-based learning of DAG…
We present an approach for synthesising observational data with elastodynamic finite element models by extending the statistical finite element method (statFEM) framework. The proposed formulation adopts a Bayesian filtering approach to…
We introduce and analyse a continuum model for an interacting particle system of Vicsek type. The model is given by a non-linear kinetic partial differential equation (PDE) describing the time-evolution of the density $f_t$, in the single…
We develop a framework for estimating unknown partial differential equations from noisy data, using a deep learning approach. Given noisy samples of a solution to an unknown PDE, our method interpolates the samples using a neural network,…
Although there is a rapidly growing literature on dynamic connectivity methods, the primary focus has been on separate network estimation for each individual, which fails to leverage common patterns of information. We propose novel…
The discovery of partial differential equations (PDEs) is a challenging task that involves both theoretical and empirical methods. Machine learning approaches have been developed and used to solve this problem; however, it is important to…
Stochastic dynamical systems provide essential mathematical frameworks for modeling complex real-world phenomena. The Fokker-Planck-Kolmogorov (FPK) equation governs the evolution of probability density functions associated with stochastic…
Federated learning (FL), which has gained increasing attention recently, enables distributed devices to train a common machine learning (ML) model for intelligent inference cooperatively without data sharing. However, problems in practical…
We propose a simple algorithm to train stochastic neural networks to draw samples from given target distributions for probabilistic inference. Our method is based on iteratively adjusting the neural network parameters so that the output…
Identifying the governing equations of a nonlinear dynamical system is key to both understanding the physical features of the system and constructing an accurate model of the dynamics that generalizes well beyond the available data. We…
We propose a new method for inferring the governing stochastic ordinary differential equations (SODEs) by observing particle ensembles at discrete and sparse time instants, i.e., multiple "snapshots". Particle coordinates at a single time…