ENME E4363 Multiscale Computational Science and Engineering (Jacob Fish)
Introduction to multiscale analysis. Information-passing bridging techniques: among them, generalized mathematical homogenization theory, the heterogeneous multiscale method, variational multiscale method, the discontinuous Galerkin method and the kinetic Monte Carlo–based methods. Concurrent multiscale techniques: domain bridging, local enrichment, and multigrid-based concurrent multiscale methods. Analysis of multiscale systems.
ECBM E4070 Computing with Brain Circuits of Model Organisms (Aurel A. Lazar)
Provides an introduction to elements of the functional logic of the fruit fly brain. Focuses on the intuitive understanding of:
(i) Functional Map of the Fruit Fly Brain,
(ii) From Odorant Transduction to Learning and Memory in Early Olfaction, and
(iii) From Sensory Coding in Early Vision to Directing Movement.
Enables the further exploration of the field of computing with brain circuits. http://www.bionet.ee.columbia.edu/courses/ECBM_E4070
APMA 4301 Numerical Methods for PDEs (Kyle T. Mandli)
Numerical solution of differential equations, in particular partial differential equations arising in various fields of application. Presentation emphasizes finite difference approaches to present theory on stability, accuracy, and convergence with minimal coverage of alternate approaches (left for other courses). Method coverage includes explicit and implicit time-stepping methods, direct and iterative solvers for boundary-value problems.
COMS 4774 unservised Learning (Daniel Hsu)
ENME 6220 Random Processes in Mechanics (Ioannis A Kougioumtzoglou)
Review of random variables. Random process theory: stationary and ergodic processes, correlations functions, power spectra. Non-stationary and non-Gaussian processes. Linear random vibration theory. Crossing rates, peak distributions, and response analysis of non-linear structures to random loading. Major emphasis on simulation of various types of random processes. Monte Carlo simulation.
APMAE4300 Introduction to Numerical Methods (Marc Spiegelman)
Introduction to fundamental algorithms and analysis of numerical methods commonly used by scientists, mathematicians and engineers. Designed to give a fundamental understanding of the building blocks of scientific computing that will be used in more advanced courses in scientific computing and numerical methods for PDEs (e.g. APMA E4301, E4302). Topics include numerical solutions of algebraic systems, linear least-squares, eigenvalue problems, solution of non-linear systems, optimization, interpolation, numerical integration and differentiation, initial value problems and boundary value problems for systems of ODE's. All programming exercises will be in Python.
ENME6332 Finite Element Analysis 2 (Haim Waisman)
APMA E4991y Applied Stochastic Analysis (Kui Ren)
EAEE 4257 Environmental Data Analysis (Bolun Xu)
Statistical methods for the analysis of the space and time structure in environmental data. Application to problems of climate variation and change; hydrology; air, water and soil pollution dynamics; disease propagation; ecological change; and resource assessment. Applications are developed using the ArcView Geographical Information System (GIS), integrated with currently available statistical packages. Team projects that lead to publication-quality analyses of data in various environmental fields of interest. An interdisciplinary perspective is emphasized in this applications-oriented class.
MECS 6616 Robot Learning (Matei Ciocarlie)
Robots using machine learning to achieve high performance in unscripted situations. Dimensionality reduction, classification and regression problems in robotics. Deep Learning: Convolutional Neural Networks for robot vision, Recurrent Neural Networks, and sensorimotor robot control using neural networks. Model Predictive Control using learned dynamics models for legged robots and manipulators. Reinforcement Learning in robotics: model-based and model-free methods, deep reinforcement learning, sensorimotor control using reinforcement learning.
ENME E6370: Turbulence Theory and Modeling (Marco Giovanni Giometto)
Turbulence phenomenology; spatial and temporal scales in turbulent flows; statistical description, filtering and Reynolds decomposition, equations governing the resolved flow, fluctuations and their energetics; turbulence closure problem for RANS and LES; two equation turbulence models and second moment closures.