Markos Katsoulakis
Professor; Director, Applied Mathematics & Computation; Director, Applied Math MS Graduate Admissions
Office Hours:
M 4-5:30PM, Th 11AM-12:30PM in LGRT 1423G or by appointment
- Markos Katsoulakis is working at the interface of Applied & Computational Mathematics and Data Science, focusing on machine learning, uncertainty quantification and applications in materials and catalysis.
- He is the Director for the Center of Applied Mathematics at the University of Massachusetts and a member of the Executive Committee of the UMASS TRIPODS Institute for Theoretical Foundations of Data Science.
- He currently serves in the Editorial Board of the SIAM/ASA Journal of Uncertainty Quantification and the Editorial Board of the SIAM Mathematical Modeling and Computation book series. He was an Associate Editor of SIAM Journal of Mathematical Analysis between 2002-2014.
- Brief CV (2024)
Education
Ph.D. Brown University, 1993
B.A. National and Kapodistrian University, 1987
RESEARCH INTERESTS
Generative Modeling, Scientific Machine Learning, Information Theory, Uncertainty Quantification, Multi-scale Methods
Teaching
Math 456.1 Fall 2024: Mathematics of Generative Artificial Intelligence
In this class, we will focus on modeling through Machine Learning and in particular on Generative Artificial Intelligence models. During the last decade, generative models have produced breakthrough results in a wide area of applications including image generation, text and speech synthesis, applications in science and engineering such as surrogate and sub-grid scale simulators (e.g. in aerospace, atmosphere ocean science and materials) and discovery of new molecules and proteins for drug design, to name only a few. In this course, we will cover to varying degrees some of the the main families of generative models such as Gaussian Mixture Models as generative models, Normalizing Flows, Generative Adversarial Networks, Variational Auto-encoders, Energy-based Models, Deep Autoregressive Models and Probabilistic Diffusion Models. We will focus on their mathematical & statistical foundations and discuss some prominent generative models and related tools. Student groups will be formed to investigate their assigned machine learning modeling project and each group will report its findings to the class in a final presentation.
Students can access the class, a detailed syllabus, slides for all lectures and other course material through Canvas
Selected Publications
- N. Mimikos-Stamatopoulos, B. J. Zhang, M. A. Katsoulakis, Score-based generative models are provably robust: an Uncertainty Quantification perspective, Thirty-Eighth Annual Conference on Neural Information Processing Systems, NeurIPS 2024
- H. Gu, P. Birmpa, Y. Pantazis, M. A. Katsoulakis, and L. Rey-Bellet, Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data, SIAM Data Science, to appear, (2024).
- B. J. Zhang, M. A. Katsoulakis, A mean-field games laboratory for generative modeling, preprint
- Z. Chen, M. A. Katsoulakis, L. Rey-Bellet, W. Zhu, Sample Complexity of Probability Divergences under Group Symmetry), International Conference on Machine Learning ICML 2023
- J. Birrell, P. Dupuis, M. A. Katsoulakis, Y. Pantazis, L. Rey-Bellet, Function-space regularized Rényi divergences, International Conference on Learning Representations ICLR 2023
- J. Birrell, P. Dupuis, M. A. Katsoulakis, Y. Pantazis, L. Rey-Bellet, (f, Γ) -Divergences: Interpolating between f-Divergences and Integral Probability Metrics, Thirty-sixth Conference on Neural Information Processing Systems NeurIPS 2022
- J. Birrell, M. A. Katsoulakis, L. Rey-Bellet, W. Zhu, Structure-preserving GANs, 39th International Conference on Machine Learning ICML 2022
- P. Birmpa, J. Feng, M. A. Katsoulakis, L. Rey-Bellet, Model Uncertainty and Correctability for Directed Graphical Models, SIAM/ASA Journal on Uncertainty Quantification 10 (4),1461-1512, (2022)
- Y. Pantazis, D. Paul, M. Fasoulakis, Y. Stylianou, M. A. Katsoulakis, Cumulant GAN, IEEE Transactions on Neural Networks and Learning Systems, (2022)
- J. Birrell, M. A. Katsoulakis, Y. Pantazis, Optimizing variational representations of divergences and accelerating their statistical estimation, IEEE Transactions on Information Theory, (2022)
- J. Birrell, P. Dupuis, M. A. Katsoulakis, Y. Pantazis, L. Rey-Bellet, (f, Γ) -Divergences: Interpolating between f-Divergences and Integral Probability Metrics, Journal of Machine Learning Research, 23 (39), 1-70, (2022).
- P. Birmpa, M. A. Katsoulakis, Uncertainty Quantification for Markov Random Fields, SIAM/ASA J. Uncertainty Quantification, 9(4), 1457–1498, (2021).
- Eric J. Hall, Søren Taverniers, Markos A. Katsoulakis, Daniel M. Tartakovsky, GINNs: Graph Informed Neural Networks for multiscale physics, J. Comp. Phys. Volume 433, 110192 (2021).
- Feng J, Lansford J, Katsoulakis M, Vlachos D. Explainable and trustworthy artificial intelligence for correctable modeling in chemical sciences, Science Advances. 2020 October 14; 6(42):eabc3204
- K. Um, E. J. Hall, M. A. Katsoulakis, D. M. Tartakovsky. Causality and Bayesian Network PDEs for multiscale representations of porous media, J. Comp. Phys. 394:658-678 (2019).
- P. Dupuis, M. A. Katsoulakis, Y. Pantazis, L. Rey-Bellet Sensitivity Analysis for Rare Events based on Renyi Divergence, Annals Applied Prob., 2020 August; 30(4):1507-1533.
- Gourgoulias K, Katsoulakis M, Rey-Bellet L, Wang J. How Biased Is Your Model? Concentration Inequalities, Information and Model Bias, IEEE Transactions on Information Theory. 2020; 66(5):3079-3097.
- P. Vilanova, M. A. Katsoulakis, Data-driven, variational model reduction of high-dimensional reaction networks, J. Comp. Phys. Volume 401, 108997 (2020)
- V. Harmandaris, E. Kalligiannaki, M. A. Katsoulakis, P. Plechac. Path-space Variational Inference for non-equilibrium coarse-grained systems, J. Comp. Phys. 314,355-383 (2016).
- P. Dupuis, M. A. Katsoulakis, Y. Pantazis, P. Plechac. Path-Space Information Bounds for Uncertainty Quantification and Sensitivity Analysis of Stochastic Dynamics, SIAM/ASA J. Uncertainty Quantification, 4(1), 80-111, (2016).
- J. E. Sutton, W. Guo, M. A. Katsoulakis & D. G. Vlachos. Effects of correlated parameters and uncertainty in electronic-structure-based chemical kinetic modelling, Nature Chemistry 8, 331–337 (2016).
- G. Arampatzis, M. A. Katsoulakis and P. Plechac, Parallelization, processor communication and error analysis in lattice kinetic Monte Carlo, SIAM Num. Analysis, 52, no. 3, 11561182, (2014).
- Y. Pantazis, D.G. Vlachos and M. A. Katsoulakis, Parametric Sensitivity Analysis for Biochemical Reaction Networks based on Pathwise Information Theory, BMC Bionformatics 14:311, (2013).
- G. Arampatzis, M. A. Katsoulakis, P. Plechác, M. Taufer, L. Xu. Hierarchical fractional step approximations and parallel kinetic Monte Carlo algorithms. J. Comp. Phys. 231, 7795-7814, (2012).
- J. Feng , M. A. Katsoulakis, A Hamilton Jacobi theory for controlled gradient flows in infinite dimensions, Arch. Rat. Mech. Analysis 192, 2 , 275-310 (2009).
- A. Sopasakis & M. A. Katsoulakis, Stochastic modeling and simulation of traffic flow: ASEP with Arrhenius look-ahead dynamics, SIAM J. Appl. Math., 66, 921-944, (2006).
- T. M. Davis, T. O.Drews, H. Ramanan, C. He, J. Dong, H. Schnablegger, M. A. Katsoulakis, E. Kokkoli, A. V. McCormick, R. L.Penn, and M. Tsapatsis. Mechanistic Principles of Nanoparticle Evolution to Zeolite Crystals, Nature Materials, 5, 400, (2006)
- A. Chaterjee, M. A. Katsoulakis & D. G. Vlachos, Binomial distribution based τ -leap accelerated stochastic simulation, J. Chem. Phys. 122, 024112 (2005)
- M. A. Katsoulakis, A. J. Majda, D. G. Vlachos. Coarse-grained stochastic processes for lattice systems, Proc. Natl. Acad. Sci. USA 100, 782-787, (2003).
- M. A. Katsoulakis & A.E. Tzavaras, Contractive Relaxation Systems and the Scalar Multidimensional Conservation Law, Comm. P.D.E. 22, (1997), 195-233.
- M. A. Katsoulakis & P. E. Souganidis, Generalized motion by mean curvature as a macroscopic limit of stochastic Ising models with long range interactions and Glauber dynamics, Comm. Math. Phys., 169, (1995), 61-97.
For a complete list see: Google Scholar page & Researchgate profile