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We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…

While the acquisition of time series has become more straightforward, developing dynamical models from time series is still a challenging and evolving problem domain. Within the last several years, to address this problem, there has been a…

Empirically observed time series in physics, biology, or medicine, are commonly generated by some underlying dynamical system (DS) which is the target of scientific interest. There is an increasing interest to harvest machine learning…

Developing surrogate geophysical models from data is a key research topic in atmospheric and oceanic modeling because of the large computational costs associated with numerical simulation methods. Researchers have started applying a wide…

Short-term load forecasting is one of the crucial sections in smart grid. Precise forecasting enables system operators to make reliable unit commitment and power dispatching decisions. With the advent of big data, a number of artificial…

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…

Accurate ocean dynamics modeling is crucial for enhancing understanding of ocean circulation, predicting climate variability, and tackling challenges posed by climate change. Despite improvements in traditional numerical models, predicting…

We present a data-efficient, multiscale framework for predicting the density profiles of confined fluids at the nanoscale. While accurate density estimates require prohibitively long timescales that are inaccessible by ab initio molecular…

Dynamic mode decomposition (DMD) gives a practical means of extracting dynamic information from data, in the form of spatial modes and their associated frequencies and growth/decay rates. DMD can be considered as a numerical approximation…

The increasing frequency of extreme weather events due to global climate change urges accurate weather prediction. Recently, great advances have been made by the \textbf{end-to-end methods}, thanks to deep learning techniques, but they face…

The representation of nonlinear sub-grid processes, especially clouds, has been a major source of uncertainty in climate models for decades. Cloud-resolving models better represent many of these processes and can now be run globally but…

The impacts of climate change are felt by most critical systems, such as infrastructure, ecological systems, and power-plants. However, contemporary Earth System Models (ESM) are run at spatial resolutions too coarse for assessing effects…

Model reduction of high-dimensional dynamical systems alleviates computational burdens faced in various tasks from design optimization to model predictive control. One popular model reduction approach is based on projecting the governing…

In this paper, we propose a predictive regression model for longitudinal images with missing data based on large deformation diffeomorphic metric mapping (LDDMM) and deep neural networks. Instead of directly predicting image scans, our…

Climate models (CM) are used to evaluate the impact of climate change on the risk of floods and strong precipitation events. However, these numerical simulators have difficulties representing precipitation events accurately, mainly due to…

Time series forecasting is a crucial challenge with significant applications in areas such as weather prediction, stock market analysis, and scientific simulations. This paper introduces an embedded decomposed transformer, 'EDformer', for…

In this paper we present a deep learning method to predict the temporal evolution of dissipative dynamic systems. We propose using both geometric and thermodynamic inductive biases to improve accuracy and generalization of the resulting…

Advances in data assimilation (DA) methods have greatly improved the accuracy of Earth system predictions. To fuse multi-source data and reconstruct the nonlinear evolution missing from observations, geoscientists are developing…

Temporal-difference (TD) networks are a class of predictive state representations that use well-established TD methods to learn models of partially observable dynamical systems. Previous research with TD networks has dealt only with…

Accurate forecasting of long-term time series has important applications for decision making and planning. However, it remains challenging to capture the long-term dependencies in time series data. To better extract long-term dependencies,…