PPT-Variational principles

and Optimality in nature Andrej Cherkaev Department of Mathematics University of Utah cherkmathutahedu USAG November 2013 Components of applied math Optimization Numerical Methods Differential equations . Gershman sjgershmprincetonedu Department of Psychology Princeton University Green Hall Princeton NJ 08540 USA Matthew D Ho64256man mdhoffmacsprincetonedu Department of Statistics Columbia University New York NY 10027 USA David M Blei bleics 1 A New Beginning 113 112 De nition of Bar Member 113 113 Variational Formulation 114 1131 The Total Potential Energy Functional 114 1132 Admissible Variations 116 1133 The Minimum Total Potential Energy Principle 116 1134 TPE Discretization 117 T Rockafellar 57th Meeting of the Indian Mathematical Society Aligarh December 2730 1991 Abstract The study of problems of maximization or minimization subject to constraints has been a fertile 64257eld for the development of mathematical analysis . Bayesian. . Inference. I:. Pattern . Recognition . and. Machine Learning. Chapter 10. Falk. . LIEDER . December. 2 2010.  . Structural. . Approximations. Statistical . Inference. Introduction. . Radar Data Assimilation for 0-12 hour severe weather forecasting. Juanzhen. Sun . National Center for Atmospheric Research. Boulder, Colorado. sunj@ucar.edu. Outline. . Background. - . Motivation . Bayesian Submodular Models. Josip . Djolonga. joint work with Andreas Krause. Motivation. inference with higher order potentials. MAP Computation . ✓. Inference? . ✘. We provide a method for inference in such models. data assimilation. and forecast error statistics. Ross Bannister, 11. th. July 2011. University of Reading, r.n.bannister@reading.ac.uk. “All models are wrong …” . (George Box). “All models are wrong and all observations are inaccurate”. 1. , Olaf Konrad. 2. , Heinz-Otto Peitgen. 1. Fast and Smooth Interactive Segmentation of Medical Images Using Variational Interpolation. 1. . Fraunhofer. MEVIS, Germany. 2. . MeVis. Medical Solutions, Germany. EGU 2012, Vienna. Michail Vrettas. 1. , Dan Cornford. 1. , Manfred Opper. 2. 1. NCRG, Computer Science, Aston University, UK. 2. Technical University of Berlin, Germany. Why do data assimilation?. Aim of data assimilation is to estimate the posterior distribution of the state of a dynamical model (X) given observations (Y). . Autoencoders. Theory and Extensions. Xiao Yang. Deep learning Journal Club. March 29. Variational. Inference. Use a simple distribution to approximate a complex distribution. Variational. parameter:. Qifeng. Chen. Stanford University. Vladlen. . Koltun. Intel Labs. Optical flow. Motion field between two image frames. Optical flow. Motion field between two image frames. Image 1. Image 2. optical flow. Inference. Dave Moore, UC Berkeley. Advances in Approximate Bayesian Inference, NIPS 2016. Parameter Symmetries. . Model. Symmetry. Matrix factorization. Orthogonal. transforms. Variational. . a. A comparison of hybrid variational data assimilation methods in the Met Office global NWP system Andrew Lorenc 11 th Adjoint Workshop, Aveiro Portugal, July 2018 www.metoffice.gov.uk © Crown Copyright 2018, Met Office Henning Lange, Mario . Bergés. , Zico Kolter. Variational Filtering. Statistical Inference. (Expectation Maximization, Variational Inference). Deep Learning. Dynamical Systems. Variational Filtering.