Abstract : Complex Systems are ubiquitous in different areas. Recent development of advanced machine learning tools and new stochastic modeling strategies introduce new insights and approaches of advancing the study of complex systems. This minisymposium aims at combining data-driven and physics-based methods to improve the current understanding, modeling and forecasting methods of various complex systems containing different features. Topics of this minisymposium include, but are not limited to, physics-driven machine learning techniques, efficient stochastic multiscale modeling approaches, data assimilation, uncertainty quantification, inverse problems, statistical control, surrogate and reduced order models as well as efficient forecast algorithms.
[03378] Generative modelling through diffusion maps
Format : Talk at Waseda University
Author(s) :
Georg A. Gottwald (University of Sydney)
Sebastian Reich (Universität Potsdam)
Fengyi Li (MIT)
Abstract : We propose a Langevin sampler as a generative modelling method. The Langevin sampler is constructed using diffusion maps. We show how this method can be used to perform inverse modelling tasks as well as providing a stochastic subgrid-scale parametrisation.
[04604] Tracer Prediction in Simplified Stochastic Geophysical Models through Kalman Filters and Related Methods
Format : Talk at Waseda University
Author(s) :
Mustafa A Mohamad (University of Calgary)
Abstract : Transport-dominated phenomena represents a major challenge for reduction techniques due to the presence of nonlinear coherent wave structures. Here we discuss the assimilation and prediction of a turbulent complex flow field given a stream of measurements provided by passively advected Lagrangian drifters. We quantify recovery of the Eulerian energy spectra from observations of Lagrangian drifters by special data assimilation algorithms. We primarily focus on algorithms based on Kalman filters, but also discuss related methods for comparison. The focus is on statistical properties of the tracer.
[05043] Machine Learning for Stochastic Parametrisation
Format : Online Talk on Zoom
Author(s) :
Hannah Christensen (University of Oxford)
Abstract : The use of stochastic techniques in atmospheric models to characterise uncertainty in small-scale processes has proved beneficial for forecasts on weather, seasonal and climate timescales. We have also recently seen significant progress in replacing the parametrisation schemes which represent these small-scale processes using machine learning (ML). This has the potential to speed up and improve numerical models. In this presentation I bring together these two developments, and discuss approaches to use ML for stochastic parametrisation.
[03280] Explainable AI to Detect, Predict and Discover Climate Variability and Change
Format : Online Talk on Zoom
Author(s) :
Elizabeth Barnes (Colorado State University)
Abstract : Earth’s climate is chaotic and noisy. Finding usable signals amidst all of the noise can be challenging: be it predicting if it will rain, knowing which direction a hurricane will go, understanding the implications of melting Arctic ice, or detecting the impacts of human-induced climate warming. Here, I will demonstrate how explainable artificial intelligence (XAI) techniques can sift through vast amounts of climate data and push the bounds of scientific discovery: allowing scientists to ask “why?” but now with the power of machine learning.
Abstract : Similarity graphs are a popular technique for semi-supervised machine learning. They have an advantage over more modern neural network methods in that they can perform well with a modest amount of training data. I will present an active learning framework in which additional training data is introduced through a human in the loop. This approach can outperform prior state of the art on several remote sensing problems such as object recognition in sythetic aperture radar and multispectral and hyperspectral imagery.
[04307] Integrating the spectral analyses of neural networks and nonlinear physics for explainability, generalizability, and stability
Format : Talk at Waseda University
Author(s) :
Pedram Hassanzadeh (Rice U)
Ashesh Chattopadhyay (PARC)
Yifei Guan (Rice U)
Adam Subel (NYU)
Abstract : I will introduce a new framework that combines the spectral (Fourier) analyses of NNs and nonlinear physics, and leverages recent advances in theory and applications of deep learning, to move toward rigorous analysis of deep NNs for applications involving dynamical systems. I will use examples from subgrid-scale modeling of 2D turbulence and Rayleigh-Bernard turbulence and forecasting extreme weather to show how this framework can be used to systematically address challenges about explainability, generalizability, and stability.
[03737] Shock trace prediction by reduced models for a viscous stochastic Burgers equation
Format : Talk at Waseda University
Author(s) :
Fei Lu (Johns Hopkins University)
Abstract : Can data-driven reduced models predict extreme events in nonlinear multiscale systems? Using stochastic Burgers equation's random shocks as a prototype of extreme events, we demonstrate that although large-scale dominating dynamics-focused reduced models cannot represent shocks, they can accurately predict shock trace—the timing and locations of shocks —with relatively low false prediction rates. The data-driven closure terms are critical in capturing unresolved small-scale dynamics' effects on resolved ones.
[01386] A Multi-Fidelity Ensemble Kalman Filter with Adaptive Reduced-Order Models
Author(s) :
Francesco Attilio Bruno Silva (Eindhoven University of Technology)
Cecilia Pagliantini (Eindhoven University of Technology)
Karen Veroy (Eindhoven University of Technology)
Abstract : Recently there has been an increased interest in combining model order reduction techniques and ensemble-based methods for state estimation of complex systems. Data assimilation algorithms have been proposed to jointly use low and high-fidelity ensembles, e.g., the MFEnKF. The construction of low-fidelity models in the offline stage, however, leads these methods into a trade-off between accuracy and computational costs. In our research, we developed adaptive reduced-basis techniques with online modified approximation spaces to mitigate this issue.
[05228] Embedding classical dynamics in a quantum computer
Format : Online Talk on Zoom
Author(s) :
Dimitrios Giannakis (Dartmouth College)
Abstract : We present a framework for simulating classical dynamical systems by quantum systems running on a quantum computer. The framework employs a quantum feature map for representing classical states by density operators on a reproducing kernel Hilbert space, $\mathcal{H}$. Simultaneously, a mapping is employed from classical observables into self-adjoint operators on $\mathcal{H}$ such that quantum expectation values are consistent with pointwise function evaluation. We illustrate our approach with quantum circuit simulations and experiments on quantum computers.
[05225] Machine learning correction operators for capturing extremes in coarse scale climate models
Format : Online Talk on Zoom
Author(s) :
Themistoklis Sapsis (MIT)
Abstract : This work presents a systematic framework for improving the predictions of statistical quantities for turbulent systems, with a focus on correcting coarse climate simulations. We also provide quantification measures for the value of data towards this goal. Machine learning correction operators for chaotic systems is challenging as learning errors due to chaotic divergence is not meaningful. The presented approach combines dynamical systems and probabilistic data-driven ideas. We apply the framework to E3SM climate simulations.
[04015] A Framework for Machine Learning of Model Error in Dynamical Systems
Format : Talk at Waseda University
Author(s) :
Matthew Levine (Caltech)
Andrew Stuart (Caltech)
Abstract : The development of data-informed predictive models for dynamical systems is of widespread interest in many disciplines. Here, we present a unifying framework for blending mechanistic and machine-learning approaches for identifying dynamical systems from data. This framework is agnostic to the chosen machine learning model parameterization, and casts the problem in both continuous- and discrete-time. We will also show recent developments that allow these methods to learn from noisy, partial observations. We first study model error from the learning theory perspective, defining the excess risk and generalization error. For a linear model of the error used to learn about ergodic dynamical systems, both excess risk and generalization error are bounded by terms that diminish with the square-root of T (the length of the training trajectory data). In our numerical examples, we first study an idealized, fully-observed Lorenz system with model error, and demonstrate that hybrid methods substantially outperform solely data-driven and solely mechanistic-approaches. Then, we present recent results for modeling partially observed Lorenz dynamics that leverages both data assimilation and neural differential equations. Joint work with Andrew Stuart.
[05032] Combining physical and machine learning forecasts for Earth system prediction
Format : Talk at Waseda University
Author(s) :
Eviatar Bach (California Institute of Technoloy)
Abstract : Machine learning (ML) holds the potential to improve Earth system prediction by learning directly from data, bypassing deficiencies in existing dynamical models. Hybrid methods, which combine ML with dynamical models, leverage the strengths of both approaches. I will present two hybrid methods that use tools from data assimilation: Ensemble Oscillation Correction, a forecasting method for combining ML forecasts of specific modes with a full-field dynamical model, and the Multi-Model Ensemble Kalman Filter, a more general method for integrating multiple forecast models with observations.
