Derek DeSantis

Jeremy Lilly, Derek DeSantis, Mark R. Petersen

Tensor train (TT) methods have recently gained popularity for accelerating the solving of systems of PDEs. Here, we evaluate the performance of TT methods in the context of geophysical fluid dynamics (GFD) using the shallow water equations and a discretization scheme employed by the ocean component of the Energy Exascale Earth System Model (E3SM). Through a suite of four test cases of increasing complexity, we evaluate TT methods in terms of how much TT is able to compress the model state, the error incurred by the TT approximation, and the speedup obtained by TT versus an optimal standard non-TT implementation in a representative subproblem. We show that though TT is able to effectively compress and speed up simple flows, it struggles to efficiently represent more complex states that are common in realistic GFD applications.

Derek DeSantis, Ayan Biswas, Earl Lawrence et al.

We propose a new method for combining in situ buoy measurements with Earth system models (ESMs) to improve the accuracy of temperature predictions in the ocean. The technique utilizes the dynamics \textit{and} modes identified in ESMs alongside buoy measurements to improve accuracy while preserving features such as seasonality. We use this technique, which we call Dynamic Basis Function Interpolation, to correct errors in localized temperature predictions made by the Model for Prediction Across Scales Ocean component (MPAS-O) with the Global Drifter Program's in situ ocean buoy dataset.

Juan Nathaniel, Carla Roesch, Jatan Buch et al.

We use a deep Koopman operator-theoretic formalism to develop a novel causal discovery algorithm, Kausal. Causal discovery aims to identify cause-effect mechanisms for better scientific understanding, explainable decision-making, and more accurate modeling. Standard statistical frameworks, such as Granger causality, lack the ability to quantify causal relationships in nonlinear dynamics due to the presence of complex feedback mechanisms, timescale mixing, and nonstationarity. This presents a challenge in studying many real-world systems, such as the Earth's climate. Meanwhile, Koopman operator methods have emerged as a promising tool for approximating nonlinear dynamics in a linear space of observables. In Kausal, we propose to leverage this powerful idea for causal analysis where optimal observables are inferred using deep learning. Causal estimates are then evaluated in a reproducing kernel Hilbert space, and defined as the distance between the marginal dynamics of the effect and the joint dynamics of the cause-effect observables. Our numerical experiments demonstrate Kausal's superior ability in discovering and characterizing causal signals compared to existing approaches of prescribed observables. Lastly, we extend our analysis to observations of El Niño-Southern Oscillation highlighting our algorithm's applicability to real-world phenomena. Our code is available at https://github.com/juannat7/kausal.

Duc P. Truong, Erik Skau, Derek Desantis et al.

A novel approach to Boolean matrix factorization (BMF) is presented. Instead of solving the BMF problem directly, this approach solves a nonnegative optimization problem with the constraint over an auxiliary matrix whose Boolean structure is identical to the initial Boolean data. Then the solution of the nonnegative auxiliary optimization problem is thresholded to provide a solution for the BMF problem. We provide the proofs for the equivalencies of the two solution spaces under the existence of an exact solution. Moreover, the nonincreasing property of the algorithm is also proven. Experiments on synthetic and real datasets are conducted to show the effectiveness and complexity of the algorithm compared to other current methods.

Derek DeSantis, Phillip J. Wolfram, Katrina Bennett et al.

A tensor provides a concise way to codify the interdependence of complex data. Treating a tensor as a d-way array, each entry records the interaction between the different indices. Clustering provides a way to parse the complexity of the data into more readily understandable information. Clustering methods are heavily dependent on the algorithm of choice, as well as the chosen hyperparameters of the algorithm. However, their sensitivity to data scales is largely unknown. In this work, we apply the discrete wavelet transform to analyze the effects of coarse-graining on clustering tensor data. We are particularly interested in understanding how scale effects clustering of the Earth's climate system. The discrete wavelet transform allows classification of the Earth's climate across a multitude of spatial-temporal scales. The discrete wavelet transform is used to produce an ensemble of classification estimates, as opposed to a single classification. Information theoretic approaches are used to identify important scale lenghts in clustering The L15 Climate Datset. We also discover a sub-collection of the ensemble that spans the majority of the variance observed, allowing for efficient consensus clustering techniques that can be used to identify climate biomes.