Related papers: A Bayesian Approach for Discovering Time- Delayed …
This work introduces an efficient novel approach for epistemic uncertainty estimation for ensemble models for regression tasks using pairwise-distance estimators (PaiDEs). Utilizing the pairwise-distance between model components, these…
In the era of Big Data, scalable and accurate clustering algorithms for high-dimensional data are essential. We present new Bayesian Distance Clustering (BDC) models and inference algorithms with improved scalability while maintaining the…
Traditional solvers for delay differential equations (DDEs) are designed around only a single method and do not effectively use the infrastructure of their more-developed ordinary differential equation (ODE) counterparts. In this work we…
An increasing number of applications require real-time reasoning under uncertainty with streaming input. The temporal (dynamic) Bayes net formalism provides a powerful representational framework for such applications. However, existing…
Modeling data obtained from dynamical systems has gained attention in recent years as a challenging task for machine learning models. Previous approaches assume the measurements to be distributed on a grid. However, for real-world…
We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…
Bayesian estimation approaches, which are capable of combining the information of experimental data from different likelihood functions to achieve high precisions, have been widely used in phase estimation via introducing a controllable…
Recent advances in stochastic differential equations (SDEs) have enabled robust modeling of real-world dynamical processes across diverse domains, such as finance, health, and systems biology. However, parameter estimation for SDEs…
The paper focuses on the numerical stability and accuracy of implicit time-domain integration (TDI) methods when applied for the solution of a power system model impacted by time delays. Such a model is generally formulated as a set of…
In view of the current availability and variety of measured data, there is an increasing demand for powerful signal processing tools that can cope successfully with the associated problems that often arise when data are being analysed. In…
In this paper, we deal with a new type of differential equations called anticipated backward doubly stochastic differential equations (anticipated BDSDEs). The coefficients of these BDSDEs depend on the future value of the solution $(Y,…
Anomalies in economic and financial data -- often linked to rare yet impactful events -- are of theoretical interest, but can also severely distort inference. Although outlier-robust methodologies can be used, many researchers prefer…
We propose practical extensions to Bayesian optimization for solving dynamic problems. We model dynamic objective functions using spatiotemporal Gaussian process priors which capture all the instances of the functions over time. Our…
The design of reliable indicators to anticipate critical transitions in complex systems is an im portant task in order to detect a coming sudden regime shift and to take action in order to either prevent it or mitigate its consequences. We…
With the rapid development of machine learning applications on time-series data, accurately assessing the value of training samples has become essential for data selection, noise detection, and model optimization. However, traditional data…
Investigating the network stability or synchronization dynamics of multi-agent systems with time delays is of significant importance in numerous real-world applications. Such investigations often rely on solving the transcendental…
Marginal-based methods achieve promising performance in the synthetic data competition hosted by the National Institute of Standards and Technology (NIST). To deal with high-dimensional data, the distribution of synthetic data is…
Model discovery aims to uncover governing differential equations of dynamical systems directly from experimental data. Benchmarking such methods is essential for tracking progress and understanding trade-offs in the field. While prior…
One of the pivotal tasks in scientific machine learning is to represent underlying dynamical systems from time series data. Many methods for such dynamics learning explicitly require the derivatives of state data, which are not directly…
Automated model discovery of partial differential equations (PDEs) usually considers a single experiment or dataset to infer the underlying governing equations. In practice, experiments have inherent natural variability in parameters,…