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Stochastic differential equations (SDEs) are a ubiquitous modeling framework that finds applications in physics, biology, engineering, social science, and finance. Due to the availability of large-scale data sets, there is growing interest…

We propose a new method for spatio-temporal forecasting on arbitrarily distributed points. Assuming that the observed system follows an unknown partial differential equation, we derive a continuous-time model for the dynamics of the data…

Accurate multistep forecasting of node-level attributes on dynamic graphs is critical for applications ranging from financial trust networks to biological networks. Existing spatiotemporal graph neural networks typically assume a static…

Robust yield curve estimation is crucial in fixed-income markets for accurate instrument pricing, effective risk management, and informed trading strategies. Traditional approaches, including the bootstrapping method and parametric…

Learning time-dependent partial differential equations (PDEs) that govern evolutionary observations is one of the core challenges for data-driven inference in many fields. In this work, we propose to capture the essential dynamics of…

In this work, we focus on variational Bayesian inference on the sparse Deep Neural Network (DNN) modeled under a class of spike-and-slab priors. Given a pre-specified sparse DNN structure, the corresponding variational posterior contraction…

Forecasting physical signals in long time range is among the most challenging tasks in Partial Differential Equations (PDEs) research. To circumvent limitations of traditional solvers, many different Deep Learning methods have been…

We present a generic framework for spatio-temporal (ST) data modeling, analysis, and forecasting, with a special focus on data that is sparse in both space and time. Our multi-scaled framework is a seamless coupling of two major components:…

Clinical time series data from electronic health records and medical registries offer unprecedented opportunities to understand patient trajectories and inform medical decision-making. However, leveraging such data presents significant…

To model time series accurately is important within a wide range of fields. As the world is generally too complex to be modelled exactly, it is often meaningful to assess the probability of a dynamical system to be in a specific state. This…

Sparse regression on a library of candidate features has developed as the prime method to discover the partial differential equation underlying a spatio-temporal data-set. These features consist of higher order derivatives, limiting model…

State-space models (SSMs) offer a powerful framework for dynamical system analysis, wherein the temporal dynamics of the system are assumed to be captured through the evolution of the latent states, which govern the values of the…

We explore the statistical and economic importance of restrictions on the dynamics of risk compensation from the perspective of a real-time Bayesian learner who predicts bond excess returns using dynamic term structure models (DTSMs). The…

Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…

Learning identifiable representations in deep generative models remains a fundamental challenge, particularly for sequential data with regime-switching dynamics. Existing approaches establish identifiability under restrictive assumptions,…

Learning unknown stochastic differential equations (SDEs) from observed data is a significant and challenging task with applications in various fields. Current approaches often use neural networks to represent drift and diffusion functions,…

The paper presents a spatio-temporal wind speed forecasting algorithm using Deep Learning (DL)and in particular, Recurrent Neural Networks(RNNs). Motivated by recent advances in renewable energy integration and smart grids, we apply our…

There is a history of simple forecast error growth models designed to capture the key properties of error growth in operational numerical weather prediction (NWP) models. We propose here such a scalar model that relies on the previous ones…

We propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central…

We present a large scale benchmark of modern deep learning architectures for a financial time series prediction and position sizing task, with a primary focus on Sharpe ratio optimization. Evaluating linear models, recurrent networks,…