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We present the Seismic Laboratory for Imaging and Modeling/Monitoring (SLIM) open-source software framework for computational geophysics and, more generally, inverse problems involving the wave-equation (e.g., seismic and medical…

Stochastic methods are a crucial area in contemporary climate research and are increasingly being used in comprehensive weather and climate prediction models as well as reduced order climate models. Stochastic methods are used as…

Projecting climate change is a generalization problem: we extrapolate the recent past using physical models across past, present, and future climates. Current climate models require representations of processes that occur at scales smaller…

Linear dynamical systems are canonical models for learning-based control of plants with uncertain dynamics. The setting consists of a stochastic differential equation that captures the state evolution of the plant understudy, while the true…

Many natural systems exhibit cyclo-stationary behavior characterized by periodic forcing such as annual and diurnal cycles. We present a data-driven method leveraging recent advances in score-based generative modeling to construct…

Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be…

We introduce a new approach to a linear-circular regression problem that relates multiple linear predictors to a circular response. We follow a modeling approach of a wrapped normal distribution that describes angular variables and angular…

Despite advances in climate modeling, simulating the El Ni\~no-Southern Oscillation (ENSO) remains challenging due to its spatiotemporal diversity and complexity. To address this, we build upon existing model hierarchies to develop a new…

We propose SLIM (Stochastic Learning and Inference in overidentified Models), a scalable stochastic approximation framework for nonlinear GMM. SLIM forms iterative updates from independent mini-batches of moments and their derivatives,…

Contrastive learning based on instance discrimination trains model to discriminate different transformations of the anchor sample from other samples, which does not consider the semantic similarity among samples. This paper proposes a new…

A continual learning (CL) algorithm learns from a non-stationary data stream. The non-stationarity is modeled by some schedule that determines how data is presented over time. Most current methods make strong assumptions on the schedule and…

Logistic models are studied as a tool to convert output from numerical weather forecasting systems (deterministic and ensemble) into probability forecasts for binary events. A logistic model obtains by putting the logarithmic odds ratio…

Time series forecasting is critical across multiple domains, where time series data exhibit both local patterns and global dependencies. While Transformer-based methods effectively capture global dependencies, they often overlook short-term…

Inverse problems are ubiquitous in the sciences and engineering. Two categories of inverse problems concerning a physical system are (1) estimate parameters in a model of the system from observed input-output pairs and (2) given a model of…

We propose a simple stochastic process for modeling improper or noncircular complex-valued signals. The process is a natural extension of a complex-valued autoregressive process, extended to include a widely linear autoregressive term. This…

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…

The control of nonlinear dynamical systems remains a major challenge for autonomous agents. Current trends in reinforcement learning (RL) focus on complex representations of dynamics and policies, which have yielded impressive results in…

Extreme environmental events such as severe storms, drought, heat waves, flash floods, and abrupt species collapse have become more prevalent in the earth-atmosphere dynamic system in recent years. In order to fully understand the…

Classical discriminant analysis assumes identically distributed training data, yet in many applications observations are collected over time and the class-conditional distributions drift. This population drift renders stationary classifiers…

Bayesian inverse problems use data to update a prior probability distribution on uncertain parameter values to a posterior distribution. Such problems arise in many structural engineering applications, but computational solution of Bayesian…