Related papers: Principled model selection for stochastic dynamics
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
In this work, an adaptive predictive control scheme for linear systems with unknown parameters and bounded additive disturbances is proposed. In contrast to related adaptive control approaches that robustly consider the parametric…
We present the particle stochastic approximation EM (PSAEM) algorithm for learning of dynamical systems. The method builds on the EM algorithm, an iterative procedure for maximum likelihood inference in latent variable models. By combining…
Often the underlying system of differential equations driving a stochastic dynamical system is assumed to be known, with inference conditioned on this assumption. We present a Bayesian framework for discovering this system of differential…
Many processes in chemistry and physics take place on timescales that cannot be explored using standard molecular dynamics simulations. This renders the use of enhanced sampling mandatory. Here we introduce an enhanced sampling method that…
A deterministic multiscale toy model is studied in which a chaotic fast subsystem triggers rare transitions between slow regimes, akin to weather or climate regimes. Using homogenization techniques, a reduced stochastic parametrization…
We study classical stochastic systems with discrete states, coupled to switching external environments. For fast environmental processes we derive reduced dynamics for the system itself, focusing on corrections to the adiabatic limit of…
The classical approach to system identification is based on stochastic assumptions about the measurement error, and provides estimates that have random nature. Worst-case identification, on the other hand, only assumes the knowledge of…
Linear mixed models are a versatile statistical tool to study data by accounting for fixed effects and random effects from multiple sources of variability. In many situations, a large number of candidate fixed effects is available and it is…
Many real-world systems are characterized by stochastic dynamical rules where a complex network of interactions among individual elements probabilistically determines their state. Even with full knowledge of the network structure and of the…
The modeling of dynamical systems is essential in many fields, but applying machine learning techniques is often challenging due to incomplete or noisy data. This study introduces a variant of stochastic interpolation (SI) for probabilistic…
A reward-guided, gradient-free ParVI method, \textit{R-ParVI}, is proposed for sampling partially known densities (e.g. up to a constant). R-ParVI formulates the sampling problem as particle flow driven by rewards: particles are drawn from…
An approach for the description of stochastic systems is derived. Some of the variables in the system are studied forward in time, others backward in time. The approach is based on a perturbation expansion in the strength of the coupling…
Stochastic kinetic models are often used to describe complex biological processes. Typically these models are analytically intractable and have unknown parameters which need to be estimated from observed data. Ideally we would have…
Stochastic modeling and simulation provide powerful predictive methods for the intrinsic understanding of fundamental mechanisms in complex biochemical networks. Typically, such mathematical models involve networks of coupled jump…
Robust physics discovery is of great interest for many scientific and engineering fields. Inspired by the principle that a representative model is the one simplest possible, a new model selection criteria considering both model's Parsimony…
In modern data analysis, sparse model selection becomes inevitable once the number of predictors variables is very high. It is well-known that model selection procedures like the Lasso or Boosting tend to overfit on real data. The…
Sparse system identification is the data-driven process of obtaining parsimonious differential equations that describe the evolution of a dynamical system, balancing model complexity and accuracy. There has been rapid innovation in system…
State-space models are dynamical systems defined by a latent and an observed process. In ecology, stochastic state-space models in discrete time are most often used to describe the imperfectly observed dynamics of population sizes or animal…
The mathematical models used to capture features of complex, biological systems are typically non-linear, meaning that there are no generally valid simple relationships between their outputs and the data that might be used to validate them.…