Talk
The science of generative models: PDEs, dynamics, and measure transport
Abstract :-
Generative modeling has recently emerged as a powerful paradigm for probabilistic modeling and inference. By enabling the synthesis of samples from complex data distributions, generative models facilitate uncertainty quantification in domains where traditional statistical approaches often struggle. This talk will present recent advances in the understanding, development, and application of generative models under the unifying framework of measure transport, with particular emphasis on dynamic parameterizations of transport. In this talk, I will analyze the behavior of diffusion models through the complementary lenses of partial differential equations (PDEs) and dynamical systems. A PDE-based perspective reveals a continuum of transport maps, while a dynamical systems analysis identifies conditions that lead to memorization. I will also introduce regularization techniques to mitigate memorization. Further, I will discuss recent progress in explicit generative modeling using classifiers — a formulation that focuses on learning population dynamics. This formulation differs from most generative models that aim to learn particle dynamics. Finally, I will demonstrate how generative models can be leveraged for data assimilation, rare-event detection and simulation, and data-driven modeling. Through examples spanning mechanical imaging, wildfire modeling, early-stage cancer detection from liquid biopsies, and state estimation in sparse, chaotic dynamical systems, I will illustrate how generative models bridge the gap between data and physics-based models to enable reliable decision-making under uncertainty. Collectively, this talk will highlight the promise of generative AI as a foundation for probabilistic reasoning, prediction, and inference in complex real-world systems.
Generative modeling has recently emerged as a powerful paradigm for probabilistic modeling and inference. By enabling the synthesis of samples from complex data distributions, generative models facilitate uncertainty quantification in domains where traditional statistical approaches often struggle. This talk will present recent advances in the understanding, development, and application of generative models under the unifying framework of measure transport, with particular emphasis on dynamic parameterizations of transport. In this talk, I will analyze the behavior of diffusion models through the complementary lenses of partial differential equations (PDEs) and dynamical systems. A PDE-based perspective reveals a continuum of transport maps, while a dynamical systems analysis identifies conditions that lead to memorization. I will also introduce regularization techniques to mitigate memorization. Further, I will discuss recent progress in explicit generative modeling using classifiers — a formulation that focuses on learning population dynamics. This formulation differs from most generative models that aim to learn particle dynamics. Finally, I will demonstrate how generative models can be leveraged for data assimilation, rare-event detection and simulation, and data-driven modeling. Through examples spanning mechanical imaging, wildfire modeling, early-stage cancer detection from liquid biopsies, and state estimation in sparse, chaotic dynamical systems, I will illustrate how generative models bridge the gap between data and physics-based models to enable reliable decision-making under uncertainty. Collectively, this talk will highlight the promise of generative AI as a foundation for probabilistic reasoning, prediction, and inference in complex real-world systems.
Speaker Bio :-
Agnimitra Dasgupta is the John von Neumann Fellow at Sandia National Laboratories. Prior to Sandia, he was a postdoctoral researcher in the Aerospace and Mechanical Engineering Department at the University of Southern California (USC). He holds a Doctor of Philosophy (PhD) in Civil Engineering from USC, awarded in 2023. Before that, he obtained a Bachelor of Engineering (BE) and a Master of Engineering (ME) in Civil Engineering from Jadavpur University and the Indian Institute of Science, respectively. His research interests focus on the intersection of computational physics, uncertainty quantification, and generative modeling. He received the Provost’s PhD Fellowship from USC from 2017 to 2021 and the Outstanding Research Assistant Award from the USC Viterbi School of Engineering in 2023.
Agnimitra Dasgupta is the John von Neumann Fellow at Sandia National Laboratories. Prior to Sandia, he was a postdoctoral researcher in the Aerospace and Mechanical Engineering Department at the University of Southern California (USC). He holds a Doctor of Philosophy (PhD) in Civil Engineering from USC, awarded in 2023. Before that, he obtained a Bachelor of Engineering (BE) and a Master of Engineering (ME) in Civil Engineering from Jadavpur University and the Indian Institute of Science, respectively. His research interests focus on the intersection of computational physics, uncertainty quantification, and generative modeling. He received the Provost’s PhD Fellowship from USC from 2017 to 2021 and the Outstanding Research Assistant Award from the USC Viterbi School of Engineering in 2023.
- 14 - 14 November,2025
- 04:00 pm - 05:00 pm
- SIT001