Center seminars are organized by the Mathematics Department and the College of Engineering. The Center gratefully acknowledges support from the UMassD Office of the Provost.
Computational Science Seminars (highlighted in gray) are technical talks on a particular research topic.
Lunchtime Computing Talks (highlighted in light blue) will introduce a new computational tool or technique to the broader UMassD community. These informal introductions assume no prior experience and will often feature a hands-on tutorial, so make sure to bring your laptops!
The Physics Colloquium series (highlighted in light red) is organized by the UMassD Department of Physics. If you are interesting in joining through zoom, please email Prof. Robert Fisher (rfisher1 - at - umassd - dot - edu) for the link.
April 27, 2022
"High-Order Operator Splitting Schemes for Stiff Differential Equations"
Abstract: Stiff differential equations are equations where fast dynamics require a strict stability restriction on our time step to prevent the error from magnifying uncontrollably. In general, stiff problems require expensive implicit solvers to avoid limiting time step restrictions. For large problems, the computational effort needed becomes increasingly prohibitive. We develop high-resolution operator splitting schemes to yield efficient, inexpensive solution approximations for stiff differential equations. To alleviate this cost, we apply a splitting technique to separate the problem into several components for simpler sequential implicit solves. We then use correction strategies to reduce errors caused by splitting, resulting in fast, accurate methods. Although the number of implicit solves increases, we show that the cost of each solve declines, resulting in an efficient scheme. By comparing the splitting scheme with classical implicit solvers, we demonstrate an increase in efficiency and recover the correct order of accuracy.
April 20, 2022
Texas A&M Institute of Data Science
"Machine Learning of Self Organization from Observation"
Abstract: Self-organization can be found in studying crystal formation, superconductivity, social behaviors, etc. It is a challenging task to understand such phenomenon from the mathematical point of view. We offer data-driven knowledge-based learning approach to interpret such phenomenon directly from observation data; moreover, our learning approach can aid in validating and improving the modeling of self-organization. We develop a convergent learning framework to derive physically meaningful dynamical systems to explain the observation of first- and second-order self-organized dynamics. Next, we study the steady state properties of our estimators. We extend the learning approach to dynamics constrained on Riemannian manifolds. Having successfully applied our learning method to simulated data sets, we study the effectiveness of our learning method on the NASA JPL's modern Ephemerides. In the end, we discuss our current research on learning interaction variables and kernels from observation, and learning from one single snapshot of observation data.