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We propose a neural network-based model for nonlinear dynamics in continuous time that can impose inductive biases on decay rates and/or frequencies. Inductive biases are helpful for training neural networks especially when training data…

Dynamical weather and climate prediction models underpin many studies of the Earth system and hold the promise of being able to make robust projections of future climate change based on physical laws. However, simulations from these models…

Ensemble Kalman methods were initially developed to solve nonlinear data assimilation problems in oceanography, but are now popular in applications far beyond their original use cases. Of particular interest is climate model calibration. As…

In this paper we survey the most recent advances in supervised machine learning and high-dimensional models for time series forecasting. We consider both linear and nonlinear alternatives. Among the linear methods we pay special attention…

Stochastic processes offer a flexible mathematical formalism to model and reason about systems. Most analysis tools, however, start from the premises that models are fully specified, so that any parameters controlling the system's dynamics…

Representing and quantifying uncertainty in physical parameterisations is a central challenge in weather and climate modelling, and approaches are often developed separately for different timescales. Here, we introduce a unified framework…

Nonlinear differential equations are encountered as models of fluid flow, spiking neurons, and many other systems of interest in the real world. Common features of these systems are that their behaviors are difficult to describe exactly and…

One of the most tedious tasks in the application of machine learning is model selection, i.e. hyperparameter selection. Fortunately, recent progress has been made in the automation of this process, through the use of sequential model-based…

In the low-data regime, it is difficult to train good supervised models from scratch. Instead practitioners turn to pre-trained models, leveraging transfer learning. Ensembling is an empirically and theoretically appealing way to construct…

We propose a novel, succinct, and effective approach for distribution prediction to quantify uncertainty in machine learning. It incorporates adaptively flexible distribution prediction of $\mathbb{P}(\mathbf{y}|\mathbf{X}=x)$ in regression…

Time series forecasting with limited data is a challenging yet critical task. While transformers have achieved outstanding performances in time series forecasting, they often require many training samples due to the large number of…

Probabilistic weather forecasts from ensemble systems require statistical postprocessing to yield calibrated and sharp predictive distributions. This paper presents an area-covering postprocessing method for ensemble precipitation…

Obtaining accurate estimates of uncertainty in climate scenarios often requires generating large ensembles of high-resolution climate simulations, a computationally expensive and memory intensive process. To address this challenge, we train…

Traditionally, weather predictions are performed with the help of large complex models of physics, which utilize different atmospheric conditions over a long period of time. These conditions are often unstable because of perturbations of…

Uncertainty estimation is important for ensuring safety and robustness of AI systems. While most research in the area has focused on un-structured prediction tasks, limited work has investigated general uncertainty estimation approaches for…

Tree-based ensemble methods such as random forests, gradient-boosted trees, and Bayesianadditive regression trees have been successfully used for regression problems in many applicationsand research studies. In this paper, we study ensemble…

We propose a framework for general probabilistic multi-step time series regression. Specifically, we exploit the expressiveness and temporal nature of Sequence-to-Sequence Neural Networks (e.g. recurrent and convolutional structures), the…

Process Outcome Prediction entails predicting a discrete property of an unfinished process instance from its partial trace. High-capacity outcome predictors discovered with ensemble and deep learning methods have been shown to achieve top…

Deep neural networks has been increasingly applied in fault diagnostics, where it uses historical data to capture systems behavior, bypassing the need for high-fidelity physical models. However, despite their competence in prediction tasks,…

Diffusion models have become increasingly popular for synthesizing high-quality samples based on training datasets. However, given the oftentimes enormous sizes of the training datasets, it is difficult to assess how training data impact…