# Applied Math Colloquium

Al Scott Lecture and Prize

TBA

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*Online*

Filtering methods for Inverse Problems

Learning and optimization tasks can be solved by modern ensemble filtering methods. A mathematical formulation as inverse problem allows to apply ensemble Kalman filter methods to obtain a gradient free, converging algorithm for general inverse problems. The analysis of the method is based on the large ensemble limit using kinetic theory. Stabilization of the method as well as numerical results will be shown in this talk.

Place: Zoom https://arizona.zoom.us/j/91826900125 Password: "Locute"

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*Online*

Output-Weighted Active Sampling for Bayesian Uncertainty Quantification and Prediction of Rare Events

We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian uncertainty quantification of rare events. The approach follows the paradigm of active learning, whereby existing samples of a black-box function are utilized to optimize the next most informative sample. The proposed method aims to take advantage of the fact that some input directions of the black-box function have a larger impact on the output than others, which is important especially for systems exhibiting rare and extreme events. The acquisition functions introduced in this work leverage the properties of the likelihood ratio, a quantity that acts as a probabilistic sampling weight and guides the active-learning algorithm towards regions of the input space that are deemed most relevant. We demonstrate superiority of the proposed approach in the uncertainty quantification of a hydrological system as well as the probabilistic quantification of rare events in dynamical systems and the identification of their precursors. We also discuss connections and implications for Bayesian optimization and present applications related to path planning for anomaly (rare event) detection in environment exploration.

Zoom: https://arizona.zoom.us/j/91826900125 Password: "Locute"

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*Online*

Physics Guided Deep Learning for Spatiotemporal Dynamics

While deep learning has shown tremendous success in many domains, it remains a grand challenge to incorporate physical principles into such models for applications in physical sciences. In this talk, I will discuss (1) Turbulent-Flow Net: a hybrid approach for predicting turbulent flow by marrying well-established computational fluid dynamics techniques with deep learning (2) Equivariant Net: a systematic approach to improve generalization of spatiotemporal models by incorporating symmetries into deep neural networks. I will demonstrate the advantage of our approaches to a variety of physical systems including fluid and traffic dynamics.

Place: Zoom https://arizona.zoom.us/j/91826900125 Password: "Locute"

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*Online*

Physical Discovery by Machine Learning: from Symmetries and Chemical Reactions to Generative and Causal Models

Machine learning has emerged as a powerful tool for the analysis of mesoscopic and atomically resolved images and spectroscopy in electron and scanning probe microscopy. The applications ranging from feature extraction to information compression and elucidation of relevant order parameters to inversion of imaging data to reconstruct structural models have been demonstrated. In this presentation, I will discuss several applications of autoencoders and variational autoencoders for the analysis of image and spectral data in STEM and SPM. The special emphasis is made on the rotationally invariant variational autoencoders that allow to disentangle rotational degrees of freedom from other latent variables in imaging and spectral data. The analysis of the latent space of autoencoders further allows establishing physically relevant transformation mechanisms. Extension of encoder approach towards establishing structure-property relationships will be illustrated on the example of ferroelectric domain walls and plasmonic structures. I will further illustrate the applications of the Bayesian inference methods towards inferring the mesoscopic and atomistic physics of materials in terms of continuous and atomistic generative models, and illustrate the pathways towards incorporation of physical models as priors within Bayesian optimization towards effective sampling of experimental parameter spaces. Ultimately, we seek to answer the causal questions such as whether frozen atomic disorder drives the emergence of the local structural distortions or average shift of the Fermi level induces structural reconstruction that in turn drive cation distribution, whether the nucleation spot of phase transition can be predicted based on observations before the transition, and what is the driving forces controlling the emergence of unique functionalities in quantum materials.

This research is supported by the by the U.S. Department of Energy, Basic Energy Sciences, Materials Sciences and Engineering Division and the Center for Nanophase Materials Sciences, which is sponsored at Oak Ridge National Laboratory by the Scientific User Facilities Division, BES DOE.

Zoom: https://arizona.zoom.us/j/91826900125 Password: "Locute"

About Sergei V. Kalinin: ergei Kalinin is a corporate fellow and a group leader at the Center for Nanophase Materials Sciences at Oak Ridge National Laboratory. He received his MS degree from Moscow State University in 1998 and Ph.D. from the University of Pennsylvania (with Dawn Bonnell) in 2002. His research presently focuses on the applications of big data and artificial intelligence methods in atomically resolved imaging by scanning transmission electron microscopy and scanning probes for applications including physics discovery and atomic fabrication, as well as mesoscopic studies of electrochemical, ferroelectric, and transport phenomena via scanning probe microscopy.

Sergei has co-authored >650 publications, with a total citation of >33,000 and an h-index of >94. He is a fellow of MRS, APS, IoP, IEEE, Foresight Institute, and AVS; a recipient of the Blavatnik Award for Physical Sciences (2018), RMS medal for Scanning Probe Microscopy (2015), Presidential Early Career Award for Scientists and Engineers (PECASE) (2009); Burton medal of Microscopy Society of America (2010); 4 R&D100 Awards (2008, 2010, 2016, and 2018); and a number of other distinctions.

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*Online*

Plasma Instabilities in the Young Solar Wind: Thermodynamics far from Equilibrium

understanding how the young solar wind expands and is accelerated and provides a natural laboratory for studying plasma physics processes that arise throughout the Universe. One key feature of the young solar wind, due to its diffuse and hot nature, is that the collision frequency is low compared to other dynamic timescales, enabling the plasma to maintain significant deviations from local thermodynamic equilibrium. In such weakly collisional systems, these departures can drive unstable wave growth and serve as signatures of wave-particle interactions that act to transfer energy between the charged particles and electromagnetic fields. In this talk, we discuss measurements of non-equilibrium solar wind structure made by spacecraft throughout the inner heliosphere, and the application of mathematical tools to infer what mechanisms, in particular instabilities, may be driven by these structures. Understanding this energy transfer will shed new light on the processes driving solar and stellar winds, heating accretion disks, and stirring the interplanetary and interstellar medium.

Place: Zoom https://arizona.zoom.us/j/91826900125 Password: "Locute"

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*Online*

Likelihood ratio methods for sensitivity analysis and linear response estimation of non-equilibrium stationary states

In many applications one is interested in estimating the response of the steady-state distribution of a stochastic dynamical system under a perturbation to the dynamics. For example, such computations form a basis for using the linear response theory of statistical mechanics in estimating transport coefficients, e.g., the mobility, the shear viscosity or the thermal conductivity, that relate the average response of the system at its steady state to an external forcing applied to the system. We briefly review a background of linear response theory and then we discuss schemes based on Girsanov's change-of-measure theory for computing the sensitivity or linear response of steady-state averages of stochastic dynamics. We discuss application of this approach to dynamics described by continuous time Markov chains as well as time homogenous Ito diffusions. We also present new schemes for estimating linear response from equilibrium fluctuations for invariant measures of Langevin dynamics. The schemes apply reweighting of trajectories by factors derived from a linearization of the Girsanov weights. We explain numerical analysis of such schemes by presenting both the discretization error and the finite time approximation error. The designed numerical schemes are shown to be of bounded variance with respect to the integration time, which is a desirable feature for long time simulations needed for steady-state sampling.

Zoom https://arizona.zoom.us/j/91826900125 Password: "Locute"

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*Online*

Brownian Dynamics Simulations for Flexible Fibers

Flexible fibers have a powerful role in microscopic biological phenomena. They can take the form of beating flagella that propel sperm cells and bacteria, or they can tangle into the vast, interconnected networks that make up the cellular cytoskeleton. In this talk I’ll discuss methods to numerically simulate flexible, inextensible microfilaments which are suspended in a viscous fluid; with special care taken to account for thermal fluctuations from the solvent. I’ll introduce a method where fibers are treated as a chain of beads and use it to interrogate experimental observations on magnetic filaments which are made to swim using an applied field. I’ll present ongoing work concerning a method more suited to fiber networks, in which inextensible fiber motions are parametrized as curves on the unit sphere. After writing down a stochastic differential equation governing the fluctuating fiber dynamics in the new, constrained coordinates, I’ll discuss temporal integration schemes which linearly scale in complexity with the number of fibers.

Zoom: https://arizona.zoom.us/j/94534134312 Password: “arizona” (all lower case)

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*Online*

Combining network analysis and persistent homology for classifying behavior of time series

Persistent homology, the flagship method of topological data analysis, can be used to provide a quantitative summary of the shape of data. One way to pass data to this method is to start with a finite, discrete metric space (whether or not it arises from a Euclidean embedding) and to study the resulting filtration of the Rips complex. In this talk, we will discuss several available methods for turning time series data into a a discrete metric space, including the Takens embedding, $k$-nearest neighbor networks, and ordinal partition networks. Combined with persistent homology and machine learning methods, we show how this can be used to classify behavior in time series in both synthetic and experimental data.

Place: Zoom https://arizona.zoom.us/j/91826900125 Password: "Locute"

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*Online*

Porous muscles: Variational methods for active porous media

Many biological organisms are comprised of deformable porous media, with additional complexity of an embedded muscle. Using geometric variational methods, we derive the equations of motion of a for the dynamics of such an active porous media. The use of variational methods allows to incorporate both the muscle action and incompressibility of the fluid and the elastic matrix in a consistent, rigorous framework, with no need to guess the balance of forces and torques. We then derive conservation laws for the motion, perform numerical simulations and show the possibility of self-propulsion of a biological organism due to particular running wave-like application of the muscle stress.

Zoom: https://arizona.zoom.us/j/91826900125 Password: "Locute"

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*Online*