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The Nelson-Siegel model is widely used in fixed income markets to produce yield curve dynamics. The multiple time-dependent parameter model conveniently addresses the level, slope, and curvature dynamics of the yield curves. In this study,…

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,…

Stochastic partial differential equations (SPDEs) are the mathematical tool of choice for modelling spatiotemporal PDE-dynamics under the influence of randomness. Based on the notion of mild solution of an SPDE, we introduce a novel neural…

We propose a novel framework for modeling the yield curve from a quantile perspective. Building on the dynamic Nelson-Siegel model of Diebold et al. (2006), we extend its traditional mean-based approach to a quantile regression setting,…

We propose a parsimonious class of arbitrage-free, yields-only dynamic term structure models (DTSMs) with unspanned latent risks. To enable sequential estimation and forecasting, we develop a Sequential Monte Carlo framework that combines…

We explore tree-based macroeconomic regime-switching in the context of the dynamic Nelson-Siegel (DNS) yield-curve model. In particular, we customize the tree-growing algorithm to partition macroeconomic variables based on the DNS model's…

Neural Ordinary Differential Equations (N-ODEs) are a powerful building block for learning systems, which extend residual networks to a continuous-time dynamical system. We propose a Bayesian version of N-ODEs that enables well-calibrated…

Latent neural stochastic differential equations (SDEs) have recently emerged as a promising approach for learning generative models from stochastic time series data. However, they systematically underestimate the noise level inherent in…

The measured spatiotemporal response of various physical processes is utilized to infer the governing partial differential equations (PDEs). We propose SimultaNeous Basis Function Approximation and Parameter Estimation (SNAPE), a technique…

Long-horizon forecasting of time-dependent partial differential equations (PDEs) is critical for characterizing the sustained evolution of physical systems. While neural operators have emerged as efficient surrogates, they typically learn…

Contemporary power grids are being challenged by rapid voltage fluctuations that are caused by large-scale deployment of renewable generation, electric vehicles, and demand response programs. In this context, monitoring the grid's operating…

Neural differential equations predict the derivative of a stochastic process. This allows irregular forecasting with arbitrary time-steps. However, the expressive temporal flexibility often comes with a high sensitivity to noise. In…

This study introduces a novel data-driven framework and the first-ever county-scale application of Spatio-Temporal Graph Neural Networks (STGNN) to forecast composite sustainability indices from herd-level operational records. The…

We introduce Neural Dynamical Systems (NDS), a method of learning dynamical models in various gray-box settings which incorporates prior knowledge in the form of systems of ordinary differential equations. NDS uses neural networks to…

Deep learning has been the engine powering many successes of data science. However, the deep neural network (DNN), as the basic model of deep learning, is often excessively over-parameterized, causing many difficulties in training,…

We introduce a novel grid-independent model for learning partial differential equations (PDEs) from noisy and partial observations on irregular spatiotemporal grids. We propose a space-time continuous latent neural PDE model with an…

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…

Many consequential real-world systems, like wind fields and ocean currents, are dynamic and hard to model. Learning their governing dynamics remains a central challenge in scientific machine learning. Dynamic Mode Decomposition (DMD)…

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…

Inspired by the ubiquitous use of differential equations to model continuous dynamics across diverse scientific and engineering domains, we propose a novel and intuitive approach to continuous sequence modeling. Our method interprets…