Research Seminars: Applied and Computational Mathematics

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

Archives

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.