Fall 2024
Time & Location: Typically talks will be in Gibson Hall 325 at 3:00 pm on a Friday.
Organizers: Chen, Hongfei and Gkogkou, Aikaterini
September 6
Title: Interpretable AI: data driven and mechanistic modeling for chemical toxicity and drug safety evaluations.
Hao Zhu - Tulane University
Abstract: Addressing the safety aspects of new chemicals has historically been undertaken through animal testing studies, which are expensive and time-consuming. Computational toxicology is a promising alternative approach that utilizes machine learning (ML) and deep learning (DL) techniques to predict toxicity potentials of chemicals. Although the applications of ML and DL based computational models in chemicals toxicity predictions are attractive, many toxicity models are “black box” in nature and difficult to interpret by toxicologists, which hampers the chemical risk assessments using these models. The recent progress of interpretable ML (IML) in the computer science field meets this urgent need to unveil the underlying toxicity mechanisms and elucidate domain knowledge of toxicity models. In this new modeling framework, the toxicity feature data, model interpretation methods, and the use of toxicity knowledgebase in IML development advance the applications of computational models in chemical risk assessments. The challenges and future directions of IML modeling in toxicology are strongly driven by heterogenous big data and newly revealed toxicity mechanisms. The big data mining, analysis, and mechanistic modeling using IML methods will advance artificial intelligence in the big data era to pave the road to future computational chemical toxicology and will have a significant impact on the risk assessment procedure and drug safety.
Time: 3:00 pm
Location: Gibson Hall 414
September13
Title: Score-Based Generative Models through the Lens of Wasserstein Proximal Operators
Siting Liu - University of California, Riverside
Abstract: In this presentation, I will discuss the essence of score-based generative models (SGMs) as entropically regularized Wasserstein proximal operators (WPO) for cross-entropy, elucidating this connection through mean-field games (MFG). The unique structure of SGM-MFG allows the HJB equation alone to characterize SGMs, demonstrated to be equivalent to an uncontrolled Fokker-Planck equation via a Cole-Hopf transform. Furthermore, leveraging the mathematical framework, we introduce an interpretable kernel-based model for the score functions, enhancing the performance of SGMs in terms of training samples and training time. The mathematical formulation of the new kernel-based models, in conjunction with the utilization of the terminal condition of the MFG, unveils novel insights into the manifold learning and generalization properties of SGMs.
If time permits, I will also discuss an inverse problem of mean-field games.
Time: 3:00 pm
Location: Gibson Hall 325
September 20
Title: TBA
TBA - University
Abstract: TBA
Time: 3:00 pm
Location: Gibson Hall 325
September 27
Title: TBA
TBA - University
Abstract: TBA
Time: 3:00 pm
Location: Gibson Hall 325
October 18
Title: Passive tracers advected by 2D Navier–Stokes equations with degenerate stochastic forcing
Keefer Rowan - NYU Courant
Abstract: I provide a high-level discussion of recent work with William Cooperman in which we prove the presence of various passive tracer phenomena in the physical model of a fluid with large-scale stirring given by the 2D Navier--Stokes equations with a degenerate stochastic forcing. This model was considered in the groundbreaking work of Hairer and Mattingly '06. The passive tracer phenomena were proved for the case of non-degenerate forcing by Bedrossian, Blumenthal, and Punshon-Smith '21, '22, '22. Our work can be viewed as a union of these frameworks.
Time: 3:00 pm
Location: Gibson Hall 325
October 25
Title: TBA
TBA - Affiliation:
Abstract: TBA
Time: 3:00 pm
Location: Gibson Hall 325
November 1
Title: TBA
TBA - Affiliation:
Abstract: TBA
Time: 3:00 pm
Location: Gibson Hall 325
November 8
Title: Multi-Physics and Multi-Model Integration with the Suite of Nonlinear and Differential/Algebraic Equation Solvers (SUNDIALS)
Steven Roberts - University: Lawrence Livermore National Laboratory (LLNL)
Abstract: Operator splitting is a simple but powerful technique to evolve coupled systems of differential equations forward in time. In the context of multi-physics simulations, where they are ubiquitous, operator splitting methods allow each process to be solved independently, possibly using a different integrator and time step tailored to the unique characteristics of that process. In this talk, I will discuss a new implementation of operator splitting methods in the SUNDIALS library and two applications. The first is a unique approach to leverage an approximate surrogate model to accelerate the integration of an expensive, full system of differential equations. Second, I will cover the benefits of high order integrators, including operator splitting, multirate, and implicit-explicit methods, for a cloud microphysics model based on a subset of the Predicted Particle Properties (P3) scheme used in the Energy Exascale Earth System Model (E3SM).
Time: 3:00 pm
Location: Gibson Hall 325
November 15
Title: TBA
TBA - Affiliation:
Abstract: TBA
Time: 3:00 pm
Location: Gibson Hall 325
November 22
Title: Existence of Stationary Measures for Sdes with Generic, Euler-Type Nonlinearities
Kyle Liss - Duke University
Abstract: Many physical phenomena involve the nonlinear, conservative transfer of energy from weakly damped degrees of freedom driven by an external force to other modes that are more strongly damped. For example, in hydrodynamic turbulence, energy enters the system primarily at large spatial scales, but at high Reynolds number, dissipative effects are only significant at very high frequencies. In this talk, I will discuss nonlinear energy transfer and the existence of invariant measures for a class of degeneratly forced SDEs on R^d with a bilinear nonlinearity B(x,x) constrained to possess various properties common to finite-dimensional fluid models and a linear damping term -Ax that acts only on a proper subset of the phase space. Existence of an invariant measure is straightforward if kerA = {0}, but when the kerA is nontrivial, an invariant measure can exist only if the nonlinearity transfers enough energy from the undamped modes to the damped modes. We develop a set of sufficient dynamical conditions on B that guarantees the existence of an invariant measure and prove that they hold “generically” within our constraint class of nonlinearities provided that dim(kerA) < 2d/3 and the stochastic forcing acts directly on at least two degrees of freedom.
Time: 3:00 pm
Location: Gibson Hall 325
December 12
Title: TBA
TBA - Affiliation:
Abstract: TBA
Time: 3:00 pm
Location: Gibson Hall 325
