Related papers: A machine learning framework for uncovering stocha…

Stochastic process discovery is concerned with deriving a model capable of reproducing the stochastic character of observed executions of a given process, stored in a log. This leads to an optimisation problem in which the model's parameter…

Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…

This paper addresses the problem of learning linear dynamical systems from noisy observations. In this setting, existing algorithms either yield biased parameter estimates or have large sample complexities. We resolve these issues by…

We present a probabilistic deep learning methodology that enables the construction of predictive data-driven surrogates for stochastic systems. Leveraging recent advances in variational inference with implicit distributions, we put forth a…

Despite extensive research, time series classification and forecasting on noisy data remain highly challenging. The main difficulties lie in finding suitable mathematical concepts to describe time series and effectively separate noise from…

Learning and forecasting stochastic time series is essential in various scientific fields. However, despite the proposals of nonlinear filters and deep-learning methods, it remains challenging to capture nonlinear dynamics from a few noisy…

Discovering governing equations that describe complex chaotic systems remains a fundamental challenge in physics and neuroscience. Here, we introduce the PEM-UDE method, which combines the prediction-error method with universal differential…

Parameter identification and comparison of dynamical systems is a challenging task in many fields. Bayesian approaches based on Gaussian process regression over time-series data have been successfully applied to infer the parameters of a…

Robust physics (e.g., governing equations and laws) discovery is of great interest for many engineering fields and explainable machine learning. A critical challenge compared with general training is that the term and format of governing…

Reconstructing high derivatives of noisy measurements is an important step in many control, identification and diagnosis problems. In this paper, a heuristic is proposed to address this challenging issue. The framework is based on a…

The vast majority of stochastic simulation models are imperfect in that they fail to exactly emulate real system dynamics. The inexactness of the simulation model, or model discrepancy, can impact the predictive accuracy and usefulness of…

Dynamical systems modeling, particularly via systems of ordinary differential equations, has been used to effectively capture the temporal behavior of different biochemical components in signal transduction networks. Despite the recent…

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…

While the Graybox characterization method allows for implicit noise models and is platform-agnostic, the method lacks uncertainty quantification. Characterization of quantum devices is a crucial process that enables researchers to gain…

This paper presents a novel machine-learning framework for reconstructing low-order gust-encounter flow field and lift coefficients from sparse, noisy surface pressure measurements. Our study thoroughly investigates the time-varying…

We introduce a robust framework for learning various generalized Hamiltonian dynamics from noisy, sparse phase-space data and in an unsupervised manner based on variational Bayesian inference. Although conservative, dissipative, and…

Macroscopic dynamical descriptions of complex physical systems are crucial for understanding and controlling material behavior. With the growing availability of data and compute, machine learning has become a promising alternative to…

Symbolic regression automates the process of learning closed-form mathematical models from data. Standard approaches to symbolic regression, as well as newer deep learning approaches, rely on heuristic model selection criteria, heuristic…

Symbolic regression is a machine learning technique that can learn the governing formulas of data and thus has the potential to transform scientific discovery. However, symbolic regression is still limited in the complexity and…

Despite rapid recent advances in quantum machine learning, the field is in many ways stuck. Existing approaches can exhibit serious limitations, and we still lack learning frameworks that are simple, interpretable, scalable, and naturally…