Research
Environmental Applications of Surrogate Modeling
Geological CO2 sequestration is an important strategy for reducing greenhouse gas emissions to the atmosphere and mitigating climate change. One of the most important assessments during the process is the coupling between mechanical deformation and fluid flow in fault zones, which is a key determinant of fault instability, induced seismicity and CO2 leakage. In this study, we develop a deep-learning-based surrogate model capable of predicting flow migration, pressure buildup and geomechanical responses in CO2 storage operations. The results highlight the importance of including uncertainty and anisotropy in realistic modeling of complex fault structures and provide more accurate scientific information for better safety management in CO2 sequestration operations.
Relevant publication: [17]
Slip tendency along the fault at t = 2, 5, 10 days.
To bridge the gap between true physics and numerical models, we explore different ML approaches in their ability to rubustly (1) emulate the complex fluid flow dynamics of the experiment; (2) infer the underlying parameters in the ground-truth physical experiments and determine the sensitivity of QoIs to these parameters; (3) generalize the reservoir geometry built in the experiment to a different geometry and injection location. In contrast with most explorations of machine learning techniques, this study relies on data from physical experiments conducted in “FluidFlower”.
Relevant publication: [20]
A digital representation of "FluidFlower"
To better understand the responses of ocean systems to different forcings that represent climate change scenarios, we have explored a wide range of values for the parameters and initial/boundary conditions in an ocean model on a global scale. Due to the complexity of global circulation models, however, simulations of ocean processes are prohibitively expensive (even on GPUs), making the tasks of uncertainty quantification for future predictions and sensitivity analysis for model parameters extremely challenging. To address this challenge, we have investigated a deep learning tools to build dynamical emulators for targeted quantities of interest (QoIs). The efficient emulators will make it possible to capture interactions between the ocean and other components of climate models (e.g., atmospheric models, land models, human activities). This provides valuable scientific information for stakeholders in fighting climate change.
Relevant publication: [21]
Snapshot of heat content in "NeverWorld", an idealized ocean model.
Reduced-Order Modeling
My Ph.D. thesis, titled “Reduced Order Models (ROMs) of Transport Phenomena”, introduces a physics-aware dynamic mode decomposition (DMD) framework, which combines the popular data-driven tool DMD with physics-aware ingredients. It ameliorates the following challenges in conventional ROMs:
Relevant publication: [4, 5, 7, 10, 13, 14, 18].
My approaches exemplify the spirit of physics-aware DMD since they account for the evolution of characteristic lines and the information about rarefactions/shocks. The resulting ROM is capable of capturing the key features of the underlying dynamics with higher-order accuracy than conventional DMD. Meanwhile, it takes but a small fraction of the computational time of other iteration-based methods (e.g., proper orthogonal decomposition), which explains its rapid adoption by engineers in fast predictions for geopotential fields, real-time control for robotic systems and for wind farms, modeling for pulsatile blood flow.
Biomedical Modeling
The COVID-19 pandemic presented enormous challenges for colleges and universities and strategies for safe reopening was a topic of debate. Many institutions that reopened cautiously in the fall 2020 experienced a massive wave of infections and colleges were soon declared as the new hotspots of the pandemic. By integrating a classical mathematical epidemiology model and Bayesian learning, we learned the dynamic reproduction number for 30 colleges from their daily case reports. Here we show that the first two weeks of instruction present a high-risk period for campus outbreaks and that these outbreaks tend to spread into the neighboring communities.
Relevant publication: [9].
Media: forbes↗, NBC news↗, fox29↗, t&f press release↗, stanford engineering↗, stanford daily↗ and 70 more. Top 5% of all research outputs scored by Altmetric.
COVID-19 cases across 30 college campuses. Reported cases for ten high case number, public, and private institutions across U.S. since the outbreak of the pandemic.
Schematic representation of our model, which predicts the temporal evolution of viral load (V ) and concentrations of plasma cells (C) and antibodies (A).
Mathematical models of in-host viral dynamics and immune response are a vital tool for patient-specific estimation of the initial viral load, prediction of the course of an infection, etc. The COVID-19 pandemics has given impetus to the development of models with an ever-increasing degree of complexity. We show that one of the most popular models—the Target Cell Limited model— fails the identifiability test, i.e., its parameters cannot be uniquely inferred from readily available data such as viral load measurements. We present a model that is both identifiable and parsimonious according to information criteria. Our model’s predictions match both reported observations of COVID-19 patients and predictions of its more complex counterparts.
Relevant publication: [12].
We present a stochastic hybrid algorithm, which combines discrete (e.g., agent-based) and continuous (e.g., PDE-based) descriptors of the dynamics of reactants with small and large numbers of molecules/agents respectively, to model a stage of the immune response to inflammation, during which leukocytes reach a pathogen via chemotaxis.
The stages of immune response to inflammation represented in our model. Left: The initial stage of inflammation. Middle: Reproduction of bacteria and release of chemoattractants by bacteria, which triggers leukocytes migration. Right: Leukocytes die either naturally or upon encountering bacteria
Relevant publication: [8]
Uncertainty Quantification of Kinetic Equations
For kinetic equations (e.g., linear transport, radiative heat transfer and chemotaxis kinetic models) with random inputs, we develop new generalized polynomial chaos (gPC)-based Asymptotic-Preserving (AP) stochastic Galerkin schemes that allow efficient computation for the problems that contain both uncertainties and multiple scales. The new schemes improve the parabolic CFL condition to a hyperbolic type when the mean free path is small, which shows significant efficiency especially in uncertainty quantification (UQ) with multi-scale problems.
Mean (left) and standard deviation (right) of a chemotaxis kinetic model with random inputs
Relevant publication: [1-3]