Abstract: Many scientific and engineering challenges, such as the design of materials or molecules or the control of experimental systems, rely on the existence of fast predictive models that can evaluate potential designs or control policies. Traditionally this has been accomplished through numerical simulation; more recently data-driven machine learning methods have been applied. However, both approaches leave gaps: physical modeling can be accurate and extrapolates well to previously-unstudied conditions, but it is often computationally expensive and relies on physics approximations that may not be valid. Machine learning can generalize from massive amounts of real-world or simulation data, but suffers from physical grounding and extrapolation into new regimes, as well as in settings where large data sets do not exist.
In this talk I explore an intermediate regime, which is hybrid reduced order models: fast simplified physics approximations where some of the unknown or approximated equations are replaced with data-driven machine learning components. Examples include coarse-grained models where the full macroscopic equations cannot be derived from first-principles microscopic equations, multiscale models with unknown closure terms or sub-grid parameterization schemes, and low-order or latent dynamical systems that learn governing equations on a low-dimensional reduced state space. I discuss how such reduced systems can be identified from very limited data, much less than is often needed in traditional machine learning but at much lower time-to-solution than traditional numerical modeling. This facilitates not only system design and control but also uncertainty quantification approaches that search the space of possible equations for predictive models that can explain the data. I will focus on an example from materials science concerning the design of self-assembling block copolymer nanomaterials.
Speaker: Dr. Nathan Urban, Applied Mathematics Department, Brookhaven National Laboratory
Location: Laufer 101
Zoom: https://stonybrook.zoom.us/j/96090260834?pwd=mw8QTHbMOw9oeU9hazZeoq8bN4VIfH.1
Meeting ID: 960 9026 0834 Passcode: 374969
In this talk I explore an intermediate regime, which is hybrid reduced order models: fast simplified physics approximations where some of the unknown or approximated equations are replaced with data-driven machine learning components. Examples include coarse-grained models where the full macroscopic equations cannot be derived from first-principles microscopic equations, multiscale models with unknown closure terms or sub-grid parameterization schemes, and low-order or latent dynamical systems that learn governing equations on a low-dimensional reduced state space. I discuss how such reduced systems can be identified from very limited data, much less than is often needed in traditional machine learning but at much lower time-to-solution than traditional numerical modeling. This facilitates not only system design and control but also uncertainty quantification approaches that search the space of possible equations for predictive models that can explain the data. I will focus on an example from materials science concerning the design of self-assembling block copolymer nanomaterials.
Speaker: Dr. Nathan Urban, Applied Mathematics Department, Brookhaven National Laboratory
Location: Laufer 101
Zoom: https://stonybrook.zoom.us/j/96090260834?pwd=mw8QTHbMOw9oeU9hazZeoq8bN4VIfH.1
Meeting ID: 960 9026 0834 Passcode: 374969