Dr. Justin Finkel

I am an applied mathematician and climate scientist, working on advancing the science of extreme weather and its relationship to climate. I draw on classic and new tools from applied mathematics to (1) sample extreme events more efficiently, (2) statistically analyze extreme weather ensembles to infer physical mechanisms and sources of predictability, and (3) inform model development as a result. Following an interest in math, physics and climate sparked during high school, I obtained a Bachelor’s degree in physics and mathematics at Washington University in St. Louis, followed by a PhD in Computational and Applied Mathematics (the first cohort) at the University of Chicago, but with a long extended visit to the Courant Institute at New York University. My PhD focused on highly idealized models of stratospheric variability, after which I moved “closer to earth” in a postdoctoral appointment at MIT, where I worked on developing rare event sampling methods for extreme precipitation. In the process, I rediscovered the value of idealized modeling. In my recently begun second postdoc back at UChicago and moving forward, I plan to leverage the hard-earned insight from both realistic and idealized ends of the model spectrum. 

A critical challenge for modern climate science is to characterize extreme weather events. From heat waves to hurricanes to cold snaps, extreme events share the common feature of being uncommon, occupying some tail of the climatic probability distribution and thus presenting only scant historical data for analysis. Such sporadically occurring events catch societies and ecosystems offguard when they do occur, and better estimating risks can help greatly to mitigate the impacts. There are several competing approaches to this challenge, each with their own tradeoffs: classical statistical methods such as extreme value theory are "universal", but limiting in their asymptotic assumptions; physical simulations can generate additional realistic data, but are expensive to run at high resolution; and machine-learned model simulations are fast but dubiously reliable, especially on extremes where training data is limited. This talk will present some Monte Carlo strategies to bring out the best in all three approaches, in particular rare event sampling (RES): a "generic" set of protocols for selectively pruning, cloning, and perturbing simulations in an ensemble to over-sample the tails while down-weighting to correct for the bias introduced. But it remains unclear how to perturb an atmospheric simulation to favor extremes that are sudden and transient---such as heavy precipitation events carried by extratropical cyclones. Such events are in a sense too predictable, resulting in under-dispersion of ensemble members. I will demonstrate this failure mode, and a simple remedy, on a hierarchy of systems from an idealized "aquaplanet" climate model to a two-dimensional channel flow to a one-dimensional chaotic system. The solution is to "try early", at a particular lead time set by the dynamics' predictability timescale, and with the right choice we achieve ~10x speedup in sampling of local, transient extremes. Crucially, the optimal timescale is not a universal quantity like the leading Lyapunov exponents, but rather must be customized for the event of interest. More generally, I argue that extreme event research should employ less random sampling and more deterministic optimization. This incidentally invites synergistic coordination between traditional physics-based codes and differentiable-by-construction machine-learned emulators. Early results on that front will also be presented. Overall, the diversity of definitions of “extreme events" and the computer models that simulate them demand commensurate flexibility in sampling methods. Rising to this challenge will be a long-term collaborative research agenda.

Seminar date and time: March 5, 2026, 1 PM ET.

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Dr. Ping-Hsuan Tsai

Dr. Ping-Hsuan Tsai is a Postdoctoral Associate in the Department of Mathematics at Virginia Tech. He received his Ph.D. in Computer Science from the University of Illinois Urbana–Champaign. His research mainly focuses on developing data-driven reduced-order models for turbulent heat transfer applications. The data collection phase involves setting up turbulent flow simulations with Nek5000/NekRS, a fast and scalable open source CFD solver, and running simulations on supercomputers. As one of the main developers, he uses NekROM - a model order reduction software package for Nek5000/NekRS, to construct reduced-order models and develop stabilizations. In order to accelerate engineering routine and design analysis, he is also working on developing error indicators to optimize the selection of training parameters (high-fidelity simulations).

Spatial filters have played a central role in large eddy simulation for many decades and, more recently, in reduced-order model (ROM) stabilization for convection-dominated flows. However, in under-resolved regimes, fundamental questions remain regarding the choice of filter and the determination of its parameters. Addressing these questions is essential for the reliable design and performance of filter-based stabilization or closure strategies. To address these issues, we propose a novel data-driven stabilization operator (StabOp) that replaces traditional spatial filters and is designed to deliver optimal accuracy for a given quantity of interest and stabilization strategy. Although the new StabOp could be used for different types of filter-based stabilization and closure, for clarity, it is investigated for the Leray ROM (L-ROM) stabilization. The StabOp is modeled as a linear, quadratic, or nonlinear neural network mapping and is trained by solving a PDE-constrained optimization problem that minimizes a prescribed loss function. Incorporating the learned operator into the L-ROM yields a new stabilized model, the StabOp-L-ROM. We assess the new StabOp-L-ROM in the numerical simulation of three convection-dominated flows in the under-resolved regime: lid-driven cavity at Re=10,000, 3D flow past a hemisphere at Re=2,200, and minimal channel flow at Re=5,000. The numerical results demonstrate that the new StabOp-L-ROM can be orders-of-magnitude more accurate than the classical L-ROM tuned with the optimal filter radius in the predictive regime. Furthermore, while the new StabOp smooths the input flow fields, its smoothing mechanism is entirely different from those of classical spatial filters.

Prof. Ameya Jagtap

I am an Assistant Professor (tenure-track) in the Department of Aerospace Engineering at Worcester Polytechnic Institute (WPI), USA. Prior to joining WPI, I served as an Assistant Professor of Applied Mathematics (Research) at Brown University for three and a half years. My academic journey includes earning both my PhD and Master's degrees in Aerospace Engineering from the esteemed Indian Institute of Science (IISc) in India. Following this, I engaged in postdoctoral research at the Tata Institute of Fundamental Research—Center for Applicable Mathematics (TIFR-CAM) in India. Subsequently, I transitioned to Brown University to continue my postdoctoral research within the Division of Applied Mathematics.

My research is uniquely positioned at the intersection of mechanical/aerospace engineering, applied mathematics, and computation. I am particularly dedicated to advancing scientific machine learning algorithms that seamlessly integrate data and physics, offering versatile applications across computational physics. My areas of expertise encompass scientific machine learning, deep learning, data- and physics-driven deep learning techniques, uncertainty quantification, and propagation, as well as multi-scale/multi-physics simulations (solids, fluids, and acoustics). I bring proficiency in spectral/finite element methods, WENO/DG schemes, and domain decomposition techniques, among others. Beyond these, I am actively engaged in more traditional machine learning algorithms such as deep generative models, and novel artificial neural network architectures, such as quantum and graph neural networks. To this end, my interests also extend to spiking neural networks and other bio-inspired computing techniques. 

TBD

Seminar date and time: TBD.

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You?

Please reach out to rmaulik@purdue.edu if you are interested in presenting in the ISCL Seminar Series! Graduate students and postdocs are particularly encouraged to present their work.

Seminar date and time: TBA.

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