www.caltech.edu Events and Seminarshttps://www.caltech.edu/campus-life-events/calendar/rss/en-usMon, 24 Apr 2023 16:00:00 -0700Graphical Designs: Structure, Complexity and Applicationshttps://www.caltech.edu/campus-life-events/calendar/hb-keller-colloquium-25Rekha R. Thomas, Walker Family Endowed Professor in Mathematics, Department of Mathematics, University of Washington
Graphical designs are quadrature rules on graphs that are discreteanalogs of spherical designs on the sphere. They have a number ofapplications to areas such as graph sampling and random walks. Animportant question about designs is how to compute/optimizeover them. I will explain how positively weighted designs can beorganized on the faces of a polytope, and how this connection can beused to compute and optimize designs in several families of graphs.The polytope connection also yields complexity results. Mon, 06 Feb 2023 16:00:00 -0800H.B. Keller Colloquium@Mon Feb 6 16:00:00 2023@main.oscweb.caltech.eduH.B. Keller ColloquiumSynthesis for robotics - what can go wrong?https://www.caltech.edu/campus-life-events/calendar/hb-keller-colloquium-26Hadas Kress-Gazit, Geoffrey S.M. Hedrick Senior Endowed Professor, Sibley School of Mechanical & Aerospace Engineering, Cornell University
Formal methods such as synthesis – automatically creating a system from a formal specification – can be leveraged to design robots and guarantee their behavior, but these guarantees do not always hold. Synthesis, while powerful, requires the designer to make assumptions about the robot and the environment in which it is operating. What happens when these assumptions are violated?In this talk I will describe how my group thinks about failures, assumption violations, and the feedback one can generate before and during task execution. Mon, 13 Feb 2023 16:00:00 -0800H.B. Keller Colloquium@Mon Feb 13 16:00:00 2023@main.oscweb.caltech.eduH.B. Keller ColloquiumAn Adjoint Method for the Nonlinear Boltzmann Equationhttps://www.caltech.edu/campus-life-events/calendar/hb-keller-colloquium-24Russel E. Caflisch, Director and Professor of Mathematics, Courant Institute of Mathematical Sciences, New York University
We present an adjoint method for the spatially homogeneous, nonlinear Boltzmann equation, for rarefied gas dynamics. The adjoint method is derived using a "discretize then optimize" approach. The discretization (in time and velocity) is the Direct Simulation Monte Carlo (DSMC) method, and adjoint equations are derived from an augmented Lagrangian. After a forward (in time) solution of DSMC, the adjoint variables are found by a backwards solver. The adjoint variable is equal to a velocity derivative of an objective function. Numerical tests show that this gives accurate velocity derivatives and can be used for optimization of the Boltzmann equation. For collision models, DSMC requires the use of an acceptance/rejection (AR) step. Discontinuities in the AR step lead to a new term, involving the so-called "score function". This is joint work with Yunan Yang and Denis Silantyev.Mon, 24 Apr 2023 16:00:00 -0700H.B. Keller Colloquium@Mon Apr 24 16:00:00 2023@main.oscweb.caltech.eduH.B. Keller Colloquium