Abstract:
Physical functionals are usually computed as solutions of variational problems
or from solutions of partial differential equations, which may require huge
computations for complex systems. Quantum chemistry calculations of molecular
energies is such an example. Machine learning algorithms do not simulate the
physical system but estimate solutions by interpolating values provided by a
training set of known examples. However, precise interpolations may require a
number of examples that is exponential in the system dimension, and are thus
intractable. This curse of dimensionality may be avoided by computing
interpolations in smaller approximation spaces, which take advantage of
physical invariants. We present a novel approach for the regression of quantum
mechanical energies based on the scattering transform of an intermediate
electron density representation. The scattering transform has the structure of
a deep convolutional network, composed of iterated wavelet transforms and
modulus operators, and possesses the appropriate invariant and stability
properties for molecular energy regression. Numerical experiments give state of
the art accuracy over data bases of planar organic molecules.
Biography:
Matthew Hirn is an assistant professor in the Department of Computational
Mathematics, Science and Engineering and the Department of Mathematics at
Michigan State University, where he has been a faculty member since 2015.
Hirn received his B.A. in mathematics from Cornell University and his Ph.D. in
mathematics from the University of Maryland, College Park. Before arriving at
Michigan State, he held postdoctoral appointments in the Department of
Mathematics at Yale University and in the Département 'Informatique at
the Ecole normale supérieure, Paris.
Hirn's research interests are at the interface of harmonic analysis and
machine learning. Broadly speaking, he develops mathematically provable machine
learning algorithms for the analysis of high dimensional data and to circumvent
prohibitively costly computations in scientific computing.
Specific research interests include:
 Applied harmonic analysis
 Manifold learning
 Smooth extensions and interpolations
 Quantum chemistry and Nbody problems
 Deep learning
 Computer vision
Host:
Dr. Metin Aktulga
