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In this work, we explore modeling change points in time-series data using neural stochastic differential equations (neural SDEs). We propose a novel model formulation and training procedure based on the variational autoencoder (VAE)…
Accurate and adaptive dynamic models are critical for underwater vehicle-manipulator systems where hydrodynamic effects induce time-varying parameters. This paper introduces a novel uncertainty-aware adaptive dynamics model framework that…
This paper proposes a novel low-rank approximation to the multivariate State-Space Model. The Stochastic Partial Differential Equation (SPDE) approach is applied component-wise to the independent-in-time Mat\'ern Gaussian innovation term in…
Long-horizon vessel trajectory forecasting under real ocean conditions is critical for collision avoidance, traffic management, and route planning. However, achieving accurate predictions is challenging due to long-range temporal…
Multiscale stochastic dynamical systems have been widely adopted to a variety of scientific and engineering problems due to their capability of depicting complex phenomena in many real world applications. This work is devoted to…
Short term load forecasting has an essential medium for the reliable, economical and efficient operation of the power system. Most of the existing forecasting approaches utilize fixed statistical models with large historical data for…
Systems governed by partial differential equations (PDEs) require computationally intensive numerical solvers to predict spatiotemporal field evolution. While machine learning (ML) surrogates offer faster solutions, autoregressive inference…
We consider the problem of forecasting complex, nonlinear space-time processes when observations provide only partial information of on the system's state. We propose a natural data-driven framework, where the system's dynamics are modelled…
Stochastic differential equations (SDEs) provide a natural framework for modelling intrinsic stochasticity inherent in many continuous-time physical processes. When such processes are observed in multiple individuals or experimental units,…
I propose a novel framework that integrates stochastic differential equations (SDEs) with deep generative models to improve uncertainty quantification in machine learning applications involving structured and temporal data. This approach,…
This paper presents a state- and control-dependent moving-horizon estimation (SCD-MHE) algorithm for nonlinear discrete-time systems. Within this framework, a pseudo-linear representation of nonlinear dynamics is leveraged utilizing state-…
Software aging is a phenomenon that affects long-running systems, leading to progressive performance degradation and increasing the risk of failures. To mitigate this problem, this work proposes an adaptive approach based on machine…
The understanding of adaptive algorithms for SDEs is an open area where many issues related to both convergence and stability (long time behaviour) of algorithms are unresolved. This paper considers a very simple adaptive algorithm, based…
Integrated wind-solar-wave marine energy systems hold broad promise for supplying clean electricity in offshore and coastal regions. By leveraging the spatiotemporal complementarity of multiple resources, such systems can effectively…
Physical systems whose dynamics are governed by partial differential equations (PDEs) find applications in numerous fields, from engineering design to weather forecasting. The process of obtaining the solution from such PDEs may be…
Predicting high-dimensional dynamical systems with irregular time steps presents significant challenges for current data-driven algorithms. These irregularities arise from missing data, sparse observations, or adaptive computational…
We introduce a class of adaptive timestepping strategies for stochastic differential equations with non-Lipschitz drift coefficients. These strategies work by controlling potential unbounded growth in solutions of a numerical scheme due to…
Learning dynamical systems from incomplete or noisy data is inherently ill-posed, as a single observation may correspond to multiple plausible futures. While physics-based ensemble forecasting relies on perturbing initial states to capture…
Non-stationarity is an intrinsic property of real-world time series and plays a crucial role in time series forecasting. Previous studies primarily adopt instance normalization to attenuate the non-stationarity of original series for better…
We develop a data-driven methodology based on parametric It\^{o}'s Stochastic Differential Equations (SDEs) to capture the real asymmetric dynamics of forecast errors. Our SDE framework features time-derivative tracking of the forecast,…