Dr. Benjamin Sanderse

Benjamin Sanderse is the group leader of the Scientific Computing group. His work focuses on development of numerical methods for uncertainty quantification, for tackling closure problems, for constructing reduced order models, with the overarching theme of using structure-preserving techniques and applying them to solve complex partial differential equations, for example occurring in fluid flow problems. Prior to his tenure track position, he worked at Shell Technology Centre Amsterdam on research and development of multiphase flow simulators in oil and gas applications. His PhD research was on new numerical methods for simulating incompressible flows occurring in wind energy applications, a combined position at Energy research Centre of the Netherlands (ECN) and CWI. He obtained his PhD degree cum laude (with honours) in 2013 from Eindhoven University of Technology. Before starting his PhD degree, he received his MSc degree in Aerospace Engineering at Delft University of Technology in 2008. For more information, please visit http://www.thinkingslow.nl.

Despite the enormous potential of generative modelling, its application to replace expensive physics simulations is still limited. One outstanding challenge in achieving efficient inference is to maintain physical consistency of the generated results. In this work, we address this challenge by leveraging the so-called stochastic interpolant framework [1] as a generative model, and incorporating energy consistency to enforce physical realism.

First, in the stochastic interpolant framework, one learns a stochastic differential equation (SDE) that maps samples from one distribution to another by defining a stochastic interpolation between the two distributions, which is then used to train a drift term in the SDE. In contrast to the widely used denoising diffusion probabilistic models, which are limited to Gaussian priors, the stochastic interpolant framework can map samples between arbitrary distributions. This is a crucial aspect, as in physics simulations (such as fluid flows), it allows us to perform time stepping from one distribution to the next without resorting to Gaussians. By applying this approach autoregressively, we can generate complete trajectories, while accounting for the inherent uncertainty by producing multiple plausible outcomes from the same initial condition.

Second, the incorporation of energy consistency, see e.g. [2], ensures that the generated trajectories adhere to the laws of physics. We demonstrate the effectiveness of our method with examples from incompressible fluid dynamics [3].

[1] M. S. Albergo, N. M. Boffi, E. Vanden-Eijnden, Stochastic interpolants: A unifying framework for flows and diffusions, arXiv preprint arXiv:2303.08797 (2023).

[2] T. van Gastelen, W. Edeling, B. Sanderse, Energy-conserving neural network for turbulence closure modeling, Journal of Computational Physics 508, 113003.

[3] N.T. Mücke, B. Sanderse, Physics-aware generative models for turbulent fluid flows through energy-consistent stochastic interpolants, arXiv:2504.05852, 2025.

Seminar date and time: October 10 (Friday), 10 AM ET.

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Prof. David Bortz

Prof. Bortz earned his PhD in 2002 with H.T. Banks at North Carolina State University. After a postdoc in Mathematics at the University of Michigan, he joined the faculty in Applied Math at the University of Colorado in 2006. The core of his research interest is in scientific computation methodologies for data-driven modeling and inverse problems at the intersection of applied math and statistics. His group has been developing a Weak-form Scientific Machine Learning framework with a wide range of applications to biology and medicine (wound healing, microbiology, epidemiology, ecology, etc.) and more recently to computational plasma physics in the context of fusion. His research has received support from NSF, NIH, DOE, and DOD.

The creation and inference of mathematical models is central to modern scientific discovery in the life sciences. As more realism is demanded of models, however, the conventional framework of biology-guided model proposal, discretization, parameter estimation, and model refinement becomes unwieldy, expensive, and computationally daunting. Recent advances in Weak form-based Scientific Machine Learning (WSciML) allow for the creation and inference of interpretable models directly from data via advanced numerical functional analysis, computational statistics, and numerical linear algebra techniques. This class of methods completely bypasses the need for forward-solve numerical discretizations and yields both parsimonious mathematical models and efficient parameter estimates. These methods are orders of magnitude faster and more accurate than traditional approaches and far more robust to the high noise levels common to data in the biological sciences. The combination of these features in a single framework provides a compelling alternative to both traditional modeling approaches as well as modern black-box neural networks. In this talk, I will present our weak form approach, describing our equation learning (WSINDy) and parameter estimation (WENDy) algorithms. I will demonstrate these performance properties via applications to several canonical problems in structured population modeling, cell migration, and mathematical epidemiology.

Seminar date and time: November 20 (Thursday), 11 AM ET.

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You?

Please reach out to rmaulik@psu.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. 10 AM ET.

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