Related papers: Dealing with Stochasticity in Biological ODE Model…

Ordinary differential equation models of biochemical reactions are often formulated as stoichiometric systems in which the dynamics arise from a collection of interacting processes. A central challenge is that the functional form of each…

Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…

Macroeconomic data is characterized by a limited number of observations (small T), many time series (big K) but also by featuring temporal dependence. Neural networks, by contrast, are designed for datasets with millions of observations and…

We describe a method for the identification of models for dynamical systems from observational data. The method is based on the concept of symbolic regression and uses genetic programming to evolve a system of ordinary differential…

The identification of a mathematical dynamics model is a crucial step in the designing process of a controller. However, it is often very difficult to identify the system's governing equations, especially in complex environments that…

We present a novel approach for training deep neural networks in a Bayesian way. Classical, i.e. non-Bayesian, deep learning has two major drawbacks both originating from the fact that network parameters are considered to be deterministic.…

Signal processing, communications, and control have traditionally relied on classical statistical modeling techniques. Such model-based methods utilize mathematical formulations that represent the underlying physics, prior information and…

We present an algorithm for model-based reinforcement learning that combines Bayesian neural networks (BNNs) with random roll-outs and stochastic optimization for policy learning. The BNNs are trained by minimizing $\alpha$-divergences,…

Boolean automata networks, genetic regulation networks, and metabolic networks are just a few examples of biological modelling by discrete dynamical systems (DDS). A major issue in modelling is the verification of the model against the…

Dynamic power system models are instrumental in real-time stability, monitoring, and control. Such models are traditionally posed as systems of nonlinear differential algebraic equations (DAEs): the dynamical part models generator…

Dosing models often use differential equations to model biological dynamics. Neural differential equations in particular can learn to predict the derivative of a process, which permits predictions at irregular points of time. However, this…

This paper explores the efficacy of diffusion-based generative models as neural operators for partial differential equations (PDEs). Neural operators are neural networks that learn a mapping from the parameter space to the solution space of…

Data-driven modeling of dynamical systems often faces numerous data-related challenges. A fundamental requirement is the existence of a unique set of parameters for a chosen model structure, an issue commonly referred to as identifiability.…

Stochastic differential equations (SDEs) are a staple of mathematical modelling of temporal dynamics. However, a fundamental limitation has been that such models have typically been relatively inflexible, which recent work introducing…

Discovering nonlinear differential equations that describe system dynamics from empirical data is a fundamental challenge in contemporary science. Here, we propose a methodology to identify dynamical laws by integrating denoising techniques…

We present a novel model Graph Neural Stochastic Differential Equations (Graph Neural SDEs). This technique enhances the Graph Neural Ordinary Differential Equations (Graph Neural ODEs) by embedding randomness into data representation using…

Equation learning aims to infer differential equation models from data. While a number of studies have shown that differential equation models can be successfully identified when the data are sufficiently detailed and corrupted with…

Identifiability is a structural property of any ODE model characterized by a set of unknown parameters. It describes the possibility of determining the values of these parameters from fusing the observations of the system inputs and…

A set of novel approaches for estimating epistemic uncertainty in deep neural networks with a single forward pass has recently emerged as a valid alternative to Bayesian Neural Networks. On the premise of informative representations, these…

Annotating the right data for training deep neural networks is an important challenge. Active learning using uncertainty estimates from Bayesian Neural Networks (BNNs) could provide an effective solution to this. Despite being theoretically…