Peng ChenSciML & UQ Group

SciML & UQ Group

Teaching

Graduate and undergraduate courses at Georgia Tech's School of Computational Science and Engineering.

Now teaching · Fall 2026

Modeling and Simulation: Foundations and Implementation

CSE 6730 / CX 4230

Time
Mondays and Wednesdays, 5:00–6:15 pm
Location
Clough Undergraduate Learning Commons 152
Office hours
Tuesdays, 2:00–3:00 pm, on Zoom (link on Canvas)
Course site
Canvas
Syllabus
CSE 6730 · CX 4230

CSE 6730 / CX 4230

Modeling and Simulation: Foundations and Implementation

  • Fall 2026
  • Fall 2025
  • Fall 2024
  • Fall 2023

This course treats modeling and simulation as the science of constructing trustworthy computational representations of natural, engineered, and computational systems. Students learn how to decide what to model, choose an appropriate simulation paradigm, construct and implement the model, determine whether the computation is correct, assess whether the model is credible for its intended purpose, and communicate what the resulting simulation can and cannot support. Classical foundations in continuous and discrete simulation are combined with selected modern topics including model reduction, uncertainty quantification, inverse problems and data assimilation, scalable simulation, scientific machine learning, and digital twins.

Three questions recur throughout the semester: What should we model? How should we simulate it? Why should anyone believe the result? A central theme of the course is therefore simulation credibility.

The goal is not merely to teach students how to run simulations. It is to teach them how to construct, interrogate, and defend computational models.

  1. real system
  2. scientific question
  3. conceptual model
  4. mathematical and computational model
  5. numerical algorithm
  6. implementation
  7. verification
  8. computational experiment
  9. validation and uncertainty
  10. prediction or decision

Schedule by week, Fall 2026

Organized around modeling questions rather than isolated algorithms.

  1. What is a computational model?

    Purposeful abstraction; states, parameters, inputs, and outputs; model hierarchy; conceptual vs. mathematical vs. computational models; verification vs. validation; credibility.

  2. Can the computer reliably evaluate our model?

    Floating point; conditioning; residual vs. error; cost and complexity; linear systems as recurring substructures.

  3. How do mechanisms become dynamical models?

    State space; conservation and balance laws; constructing ODEs; mechanistic vs. empirical models; parameter interpretation.

  4. When does a numerical trajectory represent the model?

    Euler and Runge–Kutta; local and global error; stability; stiffness; implicit vs. explicit; adaptive stepping; solver selection in practice.

  5. What qualitative behavior does the model predict?

    Equilibria; linearization; eigenvalues; phase portraits; bifurcations; chaos; separating physical from numerical instability.

  6. How do we simulate randomness and events?

    Random number generation and variates; Monte Carlo estimation and its error; discrete-event simulation: event lists, clocks, queues; worldviews.

  7. What can finite stochastic simulations tell us?

    Transient vs. steady state; warm-up bias; independent replications; output analysis; confidence intervals; variance vs. cost.

  8. When do individuals and connections matter, and how do local laws make fields? Interactive Lecture 14 →

    Agent-based and network models: paradigm selection and credibility pitfalls; conservation-based PDE construction: fluxes, constitutive laws, boundary and initial conditions.

  9. When is a computed field trustworthy, and how do we compute things that flow? Interactive Lecture 15 → · Interactive Lecture 16 →

    Finite differences for diffusion and the wave equation: consistency, stability, convergence and refinement studies, dispersion, conservation and energy checks; transport and conservation laws: CFL, numerical diffusion, the finite-volume viewpoint, shocks; shallow-water flood modeling.

  10. Expanding the PDE toolkit Interactive Lecture 17 → · Interactive Lecture 18 →

    Finite elements: weak forms, Galerkin, assembly, boundary conditions in practice; two-dimensional problems and meshes; applications to structures and tumor growth; sparse direct and iterative solvers for discretized systems.

  11. Can we replace an expensive model with a smaller one? Interactive Lecture 19 → · Interactive Lecture 20 →

    SVD and low-rank structure; POD; projection-based reduced-order models; offline and online cost; when reduction fails.

  12. How uncertain is the prediction, and what can observations identify? Interactive Lecture 21 → · Interactive Lecture 22 →

    Aleatory vs. epistemic uncertainty; Monte Carlo propagation; local and global sensitivity; inverse problems; parameter estimation; identifiability; regularization.

  13. How should observations update and justify a model?

    Bayesian inference; data assimilation; model-data discrepancy; calibration vs. validation; credibility synthesis; experimental design and multifidelity outlook.

  14. What changes at scale?

    Cost, memory, and data movement; parallelism patterns; strong and weak scaling; GPUs; a compact hands-on segment on the PACE-ICE cluster.

  15. Where do learned models belong, and does the credibility case hold?

    Surrogates; physics-informed and operator-learning concepts; digital twins as the course pipeline run continuously; a structured credibility audit of students' own projects; course synthesis.

Assessment
Six quizzes (25%), six computational laboratories (25%), and a semester team project (50%). No written final examination.
Project
Teams of 3–5 address a modeling-and-simulation problem of their choosing, from the scientific question and conceptual model through verification, validation, and a sensitivity or uncertainty study, to a reproducible repository.
Computing
Python, with a course repository of recurring case studies: epidemic models, a nonlinear oscillator, a queueing network, and heat and advection–diffusion solvers.
Prerequisites
Undergraduate calculus, elementary linear algebra, basic differential equations, basic probability, and programming.
Readings
Weekly reading notes written for the course, with references to books and papers for further study. No required textbook.
Workload
About 9–11 hours per week, including class time.

CSE 8803-IUQ

Introduction to Uncertainty Quantification

  • Spring 2026
  • Spring 2025
  • Spring 2024
  • Spring 2023

"The only thing certain in life is uncertainty." Uncertainty Quantification (UQ) is an interdisciplinary field focused on the quantitative characterization, propagation, and reduction of uncertainties. Its goal is to enable robust decision-making in the presence of the unknown, a challenge ubiquitous in essentially all science and engineering fields.

The course covers basic concepts, problem formulations, and computational algorithms, specifically focusing on:

  • Characterization: using probability models (random variables, random fields, stochastic processes);
  • Propagation: mapping input uncertainties to output solutions using Monte Carlo, Gaussian processes, and machine learning;
  • Reduction: leveraging observational data via Bayesian inference (e.g., Markov chain Monte Carlo and variational inference);
  • Decision-making: optimal control, design, and experimental design of systems via stochastic optimization under uncertainty.

It mixes a core UQ "spine" (Monte Carlo, MCMC, Gaussian processes, polynomial chaos, data assimilation, optimal experimental design) with frontier topics emphasized in the SIAM UQ community, such as generative, score, and flow methods, neural operators, transformers and in-context learning, and scalable inference. On selected Wednesdays, students present recent papers on these topics.

Topics, Spring 2026

  1. Core UQ foundations

    UQ tasks and pipeline: forward UQ, inverse problems, data assimilation, optimal experimental design, and optimization under uncertainty. Uncertainty taxonomy: aleatoric vs. epistemic; numerical error vs. model error; basic VVUQ framing. Probability and statistical computing essentials.

  2. Monte Carlo and compute-aware estimators

    Monte Carlo estimators; bias and variance; standard error and confidence intervals; convergence diagnostics. Variance reduction: control variates, importance sampling, stratification. Quasi-Monte Carlo, multilevel Monte Carlo, and multi-fidelity estimators.

  3. Reliability and sensitivity

    Rare events and reliability: failure probabilities, subset simulation and splitting methods. Sensitivity analysis: Morris screening and Sobol' indices, with their estimation and uncertainty.

  4. Surrogates, classical and modern

    Surrogate modeling and design of experiments. Polynomial chaos expansion. Gaussian process regression: kernels, hyperparameter learning, scaling, calibration. Deep and scalable Gaussian processes; Bayesian optimization and active learning.

  5. Scientific machine learning for UQ

    Neural operators (DeepONet, FNO) as operator-level surrogates, and UQ with operator surrogates. Derivative-informed and structure-exploiting operator learning. Transformers and in-context learning for PDE surrogates and inverse problems.

  6. Bayesian inference, from baseline to frontier

    Variational inference and normalizing flows. MCMC diagnostics; HMC and MALA as baseline posterior samplers. Stein and particle inference: SVGD, pSVGD, and measure flows. Generative, score, and diffusion perspectives for inverse problems and simulation-based inference.

  7. Sequential decision-making under uncertainty

    Data assimilation: state-space models, Kalman and ensemble Kalman filters, modern learned and generative directions. Bayesian optimal experimental design: utility criteria, nested expectations, surrogate acceleration, adaptive and sequential design. Optimization under uncertainty: risk-neutral vs. risk-averse objectives (CVaR, chance constraints) and surrogate-assisted optimization.

  8. Validation and communication

    Model validation, model discrepancy, and uncertainty communication: calibration and coverage, limitations, and decision-relevant reporting.

Assessment
Research project in groups of one to three (50%), paper presentation (20%), two homework assignments (20%), and participation (10%).
Prerequisites
Probability and statistics, numerical linear algebra, multivariate calculus, and numerical methods for differential equations; proficiency in Python. Prior completion of CSE 6730 or CSE/MATH 6643, or equivalent, is recommended.
Materials
No required textbook. Course slides and reading materials are provided on Canvas.
Reading list for the paper presentations, Spring 2026 38 papers

Generative, score, diffusion, and flow methods

Particle, Stein, and gradient-flow inference

Operator learning and digital-twin surrogates

Transformers and in-context learning for PDEs

Data assimilation and sequential inference

Bayesian optimal experimental design

Deep Gaussian processes and multi-fidelity modeling

UQ software and workflows