**Yaser S. Abu-Mostafa**
**
Professor of Electrical Engineering and Computer Science
**

The Learning Systems Group at Caltech studies the theory and applications of Machine Learning (ML). The theory of ML uses mathematical and statistical tools to estimate the information (data and hints) needed to learn a given task. The applications are very diverse and continue to expand to every corner of science and technology. The group works on medical applications of ML, on e-commerce and profiling applications, and on computational finance, among other domains. These applications use the latest techniques of neural networks and other models, and often give rise to novel ML theory and algorithms. Our latest projects are data-driven approach to predicting the spread of COVID-19 in every U.S. county, and ML approach to medical diagnostics using low-resolution ultrasound.

Personal Page
**Aaron Ames**
**
Bren Professor of Mechanical and Civil Engineering and Control and Dynamical Systems
**

Professor Ames’ research interests center on robotics, nonlinear control, hybrid systems and cyber-physical systems, with special emphasis on foundational theory and experimental realization on robotic systems; his lab designs, builds and tests novel bipedal robots and prosthesis with the goal of achieving human-like bipedal robotic walking and translating these capabilities to robotic assistive devices.

Personal Page
**Animashree (Anima) Anandkumar**
**
Bren Professor of Computing and Mathematical Sciences
**

Professor Anandkumar's research interests are in the areas of large-scale machine learning, non-convex optimization and high-dimensional statistics. In particular, she has been spearheading the development and analysis of tensor algorithms for machine learning. Tensor decomposition methods are embarrassingly parallel and scalable to enormous datasets. They are guaranteed to converge to the global optimum and yield consistent estimates for many probabilistic models such as topic models, community models, and hidden Markov models. More generally, Professor Anandkumar has been investigating efficient techniques to speed up non-convex optimization such as escaping saddle points efficiently.

Personal Page
**Alan H. Barr**
**
Professor of Computer Science
**

Professor Barr's research involves (1) mathematical simulation methods for computer graphics (2) developing new types of mathematical and computational methods for the study of biophysical behaviors and structures, and (3) technological leveraging for medical health care and new medical devices. In addition, he has been collaborating with JPL researcher Dr. Martin Lo on new computational and mathematical methods for utilizing the InterPlanetary Superhighway for developing new missions in the Solar System. All of these research areas involve the development and application of new mathematical and computational methods in the context of new applications in the physical sciences.

Personal Page
**Katherine L. (Katie) Bouman**
**
Assistant Professor of Computing and Mathematical Sciences, Electrical Engineering and Astronomy; Rosenberg Scholar
**

Katie Bouman's research focuses on computational imaging: designing systems that tightly integrate algorithm and sensor design, making it possible to observe phenomena previously difficult or impossible to measure with traditional approaches. Imaging plays a critical role in advancing science. However, as science continues to push boundaries, traditional sensors are reaching the limits of what they can measure. Katie's group combines ideas from signal processing, computer vision, machine learning, and physics to find and exploit hidden signals for both scientific discovery and technological innovation. For example, in collaboration with the Event Horizon Telescope, Katie's group is helping to build a computational earth-sized telescope that is taking the first images of a black hole and is analyzing its images to learn about general relativity in the strong-field regime.

Personal Page
**Oscar P. Bruno**
**
Professor of Applied and Computational Mathematics
**

Prof. Bruno's work focuses on development of accurate, high-performance numerical PDE solvers capable of modeling faithfully realistic scientific and engineering configurations. Major theoretical and computational difficulties arise in associated areas of PDE theory, numerical analysis and computational science as a result of intricate and/or singular geometries as well as solution singularities, resonances, nonlinearities, high-frequencies, dispersion, etc. Recently developed Fourier Continuation (FC) and integral-equation techniques, which can successfully tackle such challenges, have enabled accurate solution of previously intractable PDE problems of fundamental importance in science and engineering.

Personal Page
**Joel W. Burdick**
**
Richard L. and Dorothy M. Hayman Professor of Mechanical Engineering and Bioengineering; Jet Propulsion Laboratory Research Scientist
**

Professor Burdick focuses on robotics, kinematics, mechanical systems and control. Active research areas include: robotic locomotion, sensor-based motion planning algorithms, multi-fingered robotic manipulation, applied nonlinear control theory, neural prosthetics, and medical applications of robotics.

Research Group
**Venkat Chandrasekaran**
**
Professor of Computing and Mathematical Sciences and Electrical Engineering
**

Chandrasekaran’s research interests broadly lie in mathematical optimization and its interface with topics in the information sciences. Specific areas of interest include convex optimization, mathematical signal processing, graphs and combinatorial optimization, applied algebraic geometry, computational harmonic analysis, and statistical inference.

Personal Page
**Soon-Jo Chung**
**
Bren Professor of Aerospace and Control and Dynamical Systems; Jet Propulsion Laboratory Research Scientist
**

Professor Chung's research focuses on distributed spacecraft systems, space autonomous systems, and aerospace robotics, and in particular, on the theory and application of complex nonlinear dynamics, control, estimation, guidance, and navigation of autonomous space and air vehicles.

Research Group
**Mathieu Desbrun**
**
Carl F Braun Professor of Computing and Mathematical Sciences
**

Applied geometry (geometry processing, meshing, and computer graphics); Discrete differential modeling (differential, yet readily-discretizable tools for computational modeling); finite element modeling.

Personal Page
**John Doyle**
**
Jean-Lou Chameau Professor of Control and Dynamical Systems, Electrical Engineering, and Bioengineering
**

Doyle's research is on theoretical foundations for complex tech, bio, med, neuro, and social networks integrating control, communications, computing, and multiscale physics. Layered architectures such as brains integrate high level planning with fast lower level sensing, reflex, and action and facilitate learning, adaptation, augmentation (tools), and teamwork, despite being implemented in energy efficient hardware with sparse, quantized, noisy, delayed, and saturating sensing, communications, computing, and actuation, on time scales from milliseconds to minutes to days. We are developing a mathematical framework that deals with all of these features and constraints in a coherent and rigorous way with broad applications in science, technology, ecology, and society.

Personal Page
**Babak Hassibi**
**
Mose and Lillian S. Bohn Professor of Electrical Engineering and Computing and Mathematical Sciences
**

Hassibi's research spans various aspects of information theory, signal processing, control theory, and machine learning. He has made contributions to the theory and practice of wireless communications and wireless networks, as well as to robust control, adaptive filtering and neural networks, network information theory, coding for control, phase retrieval, structured signal recovery, high dimensional statistics, epidemic spread in complex networks, and DNA micro-arrays. On the mathematical side, he is interested in linear algebra, with an emphasis on fast algorithms, random matrices, and group representation theory.

Research Group
**Thomas Y. Hou**
**
Charles Lee Powell Professor of Applied and Computational Mathematics
**

Professor Hou focuses on multiscale problems arising from geophysical applications and fluid dynamics, the Millennium Problem on the 3D incompressible Navier-Strokes equations, model reduction for stochastic problems with high dimensional input variables, and adaptive data analysis.

Personal Page
**Victoria Kostina**
**
Professor of Electrical Engineering and Computing and Mathematical Sciences
**

Victoria Kostina's research spans information theory, coding, and wireless communications. Her current efforts explore one of the most exciting avenues in today's information theory: the nonasymptotic regime. Leveraging tools from the theory of random processes and concentration of measure, she pursues fundamental insight into modern delay-constrained communication systems.

Research Group
**Steven Low**
**
Frank J. Gilloon Professor of Computing and Mathematical Sciences and Electrical Engineering
**

Power systems, cyber-physical systems, network architecture, energy-efficient networking.

Personal Page
**Urmila Mahadev**
**
Assistant Professor of Computing and Mathematical Sciences
**

Mahadev's broad theme of research is in cryptographic possibilities of quantum information, a topic of considerable interest in the field. She has built new quantum cryptographic primitives by adapting and extending techniques from modern classical cryptography and has pioneered two widely acclaimed fundamental breakthroughs: 1) Quantum homomorphic encryption (i.e., computing on encrypted data) and 2) Verifiable delegation of quantum computation. Mahadev plans to focus her future research efforts on exploring problems in the intersection of theoretical computer science and quantum computing.

**Dan Meiron**
**
Fletcher Jones Professor of Aeronautics and Applied and Computational Mathematics
**

Professor Meiron's research focuses on computation and modelling of basic fluid mechanical phenomena. Particular interests include shock driven flow instabilities, turbulence, simulation approaches for high strain rate solid mechanics. He is also interested on development of adaptive numeriocal methods for such flows that are suitable for high performance computation.

Research Group
**Richard M. Murray**
**
Thomas E. and Doris Everhart Professor of Control and Dynamical Systems and Bioengineering; William K. Bowes Jr. Leadership Chair, Division of Biology and Biological Engineering
**

Research in Richard Murray's group is in the application of feedback and control to networked systems, with applications in biology and autonomy. Current projects include novel control system architectures, biomolecular feedback systems and networked control systems.

Personal Page
**Houman Owhadi**
**
Professor of Applied and Computational Mathematics and Control and Dynamical Systems
**

Professor Owhadi’s research concerns the exploration of interplays between numerical approximation, statistical inference and learning from a game theoretic perspective. Whereas the process of discovery is usually based on a combination of trial and error, insight and plain guesswork, his research is motivated by the facilitation/automation possibilities emerging from these interplays.

Personal Page
**Lior Pachter**
**
Bren Professor of Computational Biology and Computing and Mathematical Sciences
**

Professor Patcher is a computational biologist working in genomics. His career began in comparative genomics, and initially was interested in genome alignment, annotation, and the determination of conserved regions using phylogenetic methods. More recently he's become focused on functional genomics, which includes answering questions about the function and interaction of DNA, RNA and protein products. He's particularly interested in applications of high-throughput sequencing to RNA biology. Genomics requires the development of algorithms, statistical methodology and mathematical foundations, and a major part of his research is therefore on methods.

Personal Page
**Niles A. Pierce**
**
Professor of Applied and Computational Mathematics and Bioengineering; Executive Officer for Biology and Biological Engineering
**

Engineering small conditional DNAs and RNAs for signal transduction in vitro, in situ, and in vivo; computational algorithms for the analysis and design of nucleic acid structures, devices, and systems; programmable molecular technologies for readout and regulation of the state of endogenous biological circuitry.

Research Group
**Peter Schroeder**
**
Shaler Arthur Hanisch Professor of Computer Science and Applied and Computational Mathematics
**

Professor Schröder is interested in the design of efficient and reliable algorithms for problems in computer graphics. These range from geometric modeling (effective methods to model the shape of objects) to animation (simulation of physical phenomena such as the deformation of cloth). His emphasis is on an area known as "Discrete Differential Geometry." Its goals are to rebuild the foundations of classical differential geometry in a discrete setting which makes it immediately useful for computation.

**Leonard J. Schulman**
**
Professor of Computer Science
**

Algorithms and Communication Protocols; Combinatorics and Probability; Coding and Information Theory; Quantum Computation.

Personal Page
**Andrew Stuart**
**
Bren Professor of Computing and Mathematical Sciences
**

Professor Stuart's research is focused on the development of mathematical and algorithmic frameworks for the seamless integration of models with data. He works in the Bayesian formulation of inverse problems, and in data assimilation for dynamical systems. Quantification of uncertainty plays a significant role in this work. Current applications of interest include a variety of problems in the geophysical sciences, and in graph-based learning.

Research Group
**Joel A. Tropp**
**
Steele Family Professor of Applied and Computational Mathematics
**

Joel Tropp's work lies at the interface of applied mathematics, electrical engineering, computer science, and statistics. This research concerns the theoretical and computational aspects of data analysis, sparse modeling, randomized linear algebra, and random matrix theory.

Research Group
**Christopher Umans**
**
Professor of Computer Science; Executive Officer for Computing and Mathematical Sciences
**

Professor Umans is interested in theoretical computer science, and especially computational complexity. He enjoys problems with an algebraic flavor, and this often leads to research questions in derandomization and explicit combinatorial constructions, algebraic algorithms, coding theory, and hardness of approximation.

Personal Page
**Thomas Vidick**
**
Professor of Computing and Mathematical Sciences
**

Professor Vidick’s research is situated at the interface of theoretical computer science, quantum information and cryptography. He is interested in applying techniques from computer science, such as complexity theory, to study problems in quantum computing. He has investigated the role of entanglement in multi-prover interactive proof systems and obtained the first substantial computational hardness results on the power of entangled provers. Entanglement also plays a major role in quantum cryptography, and he has made important contributions to the field of device-independent cryptography. He is also interested in using quantum information theory to shed new light on fundamental techniques in theoretical computer science such as semidefinite programming and approximation algorithms.

Personal Page
**Adam Wierman**
**
Professor of Computing and Mathematical Sciences; Director, Information Science and Technology
**

Adam Wierman's research interests center around resource allocation and scheduling decisions in computer systems and services. More specifically, his work focuses both on developing analytic techniques in stochastic modeling, optimization, machine learning, and game theory, and applying these techniques to application domains such as energy-efficient computing, the cloud, the smart grid, and social networks.

Personal Page
**Erik Winfree**
**
Professor of Computer Science, Computation and Neural Systems, and Bioengineering
**

Professor Winfree's research involves theoretical and experimental aspects of molecular programming. Models of computation are developed that incorporate essential features of molecular folding, molecular self-assembly, biochemical circuits, and molecular robotics. These models are studied to determine their expressiveness for programming molecular-level tasks including decision-making, memory, behavior, and morphogenesis. Methods for compiling abstract molecular programs into actual molecules are developed and tested in the laboratory.

Personal Page
**Yisong Yue**
**
Professor of Computing and Mathematical Sciences
**

Yisong Yue's research interests lie primarily in the theory and application of statistical machine learning. He is particularly interested in developing novel methods for interactive machine learning and structured machine learning. In the past, his research has been applied to information retrieval, recommender systems, text classification, learning from rich user interfaces, analyzing implicit human feedback, clinical therapy, tutoring systems, data-driven animation, behavior analysis, sports analytics, experiment design for science, learning to optimize, policy learning in robotics, and adaptive planning & allocation problems.

Personal Page