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Links : Interdisciplinary Center for Quantitative Modeling in Biology (ICQMB) seminar

             UCR Math Department seminar                IF: 11.1 Q1 B1

In Winter 2024, the PDE & Applied Math seminar will be held through Zoom or in person (Skye 268). Specific information about the format of each talk will be provided in the email announcement and posted below. If you're interested in attending the seminar, please contact Dr. Weitao Chen (weitaoc@ucr.edu) and Dr. Maziar Raissi (maziarr@ucr.edu).

Winter 2024 Schedule 

Jan 10 10:00 AM (Wed) Ehud Yariv (Technion - Israel Institute of Technology) 

Jan 16 10:00 (Tue) Siting Liu (University of California, Los Angeles)

Jan 17 10:00 (Wed) Herve Nganguia (Towson University) 

Jan 22 10:00 AM (Mon) Mitchel Colebank (University of California, Irvine) 

Jan 24 10:00 AM (Wed) Yuchi Qiu (University of California, Irvine) 

Jan 25 10:00 AM (Thu) Daniel Gomez (University of Pennsylvania)

Feb 7  4:00 PM (Wed) Chi-Wang Shu (Brown University) (Department Colloquium)

Feb 14 10:00 AM (Wed) Liu Yang (University of California, Los Angeles)

Feb 21 1:00 PM (Wed) Stacey Finley (University of Southern California) (Distinguished Lecture of ICQMB)

Feb 28 11:00 AM (Wed) Max Hill (University of California, Riverside) (Combinatorics, Number Theory Seminar)

Mar 6  10:00 AM (Wed) Max Hill (University of California, Riverside) (Combinatorics, Number Theory Seminar)

Mar 13 10:00 AM (Wed) Arif Badrou (University of California, Riverside)

Upcoming Talk:

March 13, 2024, 10:00 AM - 10:50 AM PT 

Dr. Arif Badrou (Department of Mechanical Engineering, University of California, Riverside)

Title: Advancing Computational Lung Models through Experimental Investigations

Abstract: Diseases affecting the lungs, such as Covid-19 and Chronic Obstructive Pulmonary Disease (COPD), are significant contributors to global mortality and morbidity. Exploring the inherent mechanisms of breathing has the potential to progress both the diagnosis and treatment of these conditions. In this talk, I will share our group's research on lung mechanics, which integrates both experimental and numerical investigations. On a first part, I will delve into the experimental studies conducted on various lung components across different species, including mice, rats, pigs, and humans. Notably, our lab has developed a custom-designed pressure-volume

ventilation system coupled with cameras to capture displacements and strains through Digital Image Correlation (DIC) techniques. Furthermore, our laboratory conducts comprehensive investigations utilizing biaxial tensile tests and indentation measurements at the tissue level. These studies offer valuable insights into the mechanical properties of different components constituting the lung. The experimental data serves as crucial input for informing Finite Element (FE) Models of lungs. To illustrate, I will provide two examples. The first example will focus on the development of a reduced-order surface model of a pig lung specimen, informed, and validated by 3D DIC. Building upon this, we have developed a poroelastic model of a human lung that integrates the intricate airway network and accounts for pressure distribution during diverse breathing patterns. The calibration of this model involves utilizing the previously mentioned continuous experimental measurements and the inverse FE method. In conclusion, I will discuss the significance of such models in advancing pulmonary research and computational medicine in general.

Title and Abstracts:

Jan 10, 2024, 10:00 AM - 10:50 AM PT 

Dr. Ehud Yariv (Technion - Israel Institute of Technology)

Title: Shocks and caps in Taylor-Melcher electrohydrodynamics

Abstract: The problem of electrohydrodynamic drop deformation is well understood in the case where the external electric field is weak. In one of his many celebrated papers (Proc. R. Soc. A, 291 1425 159-166, 1966), G. I. Taylor worked out a complete theory in this limit, including analytical expressions for the electrohydrodynamic flow engendered within and outside of the drop by the electric field acting on its own induced interfacial charge.

In this talk, we will employ numerical and asymptotic tools to explore the effects of interfacial-charge convection, which were neglected by Taylor but become important at strong electric fields. In particular, we will analyze (in 2D, for simplicity) how Taylor’s fore-aft symmetric solution evolves as the electrical Reynolds number is increased from zero to arbitrarily large values. What we shall find is hinted by the title of the talk. We will discuss connections between our results, numerical evidence in the literature for the formation of equatorial interfacial-charge “shocks” (a term which we shall challenge), and strong-field experiments exhibiting equatorial streaming, pattern formation and transition to spontaneous drop rotation.

Jan 16, 2024, 11:30 AM - 12:30 PM PT 

Dr. Siting Liu (UCLA)

Title: Enhancing PDE computations and Score-based Generative Models through Optimization

Abstract: This presentation explores optimization strategies for improving both partial differential equations (PDE) and score-based generative models (SGM). In the realm of numerical computations, we introduce a saddle point framework that capitalizes on the inherent structure of PDEs. Integrated seamlessly with existing discretization schemes, this framework eliminates the necessity for nonlinear inversions, paving the way for efficient parallelization. Shifting our focus to SGM, we delve into the mathematical foundations of the Wasserstein proximal operator (WPO). Specifically, we express it as the Wasserstein proximal operator of cross-entropy. By leveraging the PDE formulation of WPO, we propose a WPO-informed score model that demonstrates accelerated training and reduced data requirements.  

Jan 17, 2024, 4:00 AM - 5:00 PM PT 

Dr. Herve Nganguia (Towson University)

Title: Towards a multi-scale mathematical model for drug delivery systems

Abstract: Drug delivery systems (DDS) are revolutionizing modern medicine and present the most promising therapeutic alternatives to treat illnesses while minimizing side effects. In experiments and clinical trials, they have been proven particularly useful in the management of effective cancer medications and therapies that are also highly toxic for healthy cells. Beyond their biomedical potential, the design, deployment and control of DDS represent an interesting (and indeed fascinating) multi-scale mathematical modeling problem. I will start my presentation with a brief survey of laboratory experiments illustrating the range of drug delivery machines design, followed by a discussion of the various components involved in this practical application of mathematical and physical methods. The rest of the talk will be devoted to a couple of recent modeling efforts related to DDS' design and propulsion in biologically relevant flows.

Jan 22, 2024, 4:00 AM - 5:00 PM PT 

Dr. Mitchel Colebank (University of California, Irvine)

Title: Computational Modeling and Statistical Inference for Cardiovascular Digital Twins

Abstract: Cardiovascular disease is the leading cause of death in the modern world and acts on multiple spatial and temporal scales. Computational models have had notable success in simulating cardiovascular function and integrating multimodal data from either pre-clinical or clinical studies. The development of subject-specific models informed by these data sources are necessary for establishing cardiovascular digital twins for clinical patient management. However, functional data (e.g., invasive hemodynamics) as well as structural imaging data are both subjected to measurement error but are necessary for model calibration and parameter inference. Thus, cardiovascular digital twins must include mathematical models of multiscale, physiological mechanisms, as well as robust statistical methods for parameter inference and uncertainty quantification. Surrogate modeling is also necessary to overcome the computational expense of these multiscale models and enable nearly real time predictions. In this talk, I will discuss innovations in image-based models of blood flow (described by partial differential equations), multiscale systems-level models of cardiac function (systems of ordinary differential equations), and the statistical tools necessary for inverse problems and uncertainty quantification in cardiovascular research. While a majority of the work will focus on pulmonary vascular and right heart function, these methods collectively build the necessary tools for developing digital twins for multiple cardiac and vascular sub-units of the full cardiovascular system.

Jan 24, 2024, 4:00 AM - 5:00 PM PT 

Dr. Yuchi Qiu (University of California, Irvine)

Title: Multiscale modeling and topological data analysis in artificial intelligence-driven biology

Abstract: Artificial intelligence (AI) has emerged as a pivotal tool in biology, revolutionizing data analysis at both large-scale and single-cell levels. However, the lack of interpretability in Al poses challenges in extracting intricate functions and dynamics from high-dimensional, complex heterogeneous,and noisy biological data. In this talk, we aim to address these challenges by investigating dynamics and topology of data via multiscale modeling and topological data analysis. First, we will discuss our approaches for deciphering cellular spatio-temporal dynamics, focusing on the interplay between gene regulation, spatial signals, and intercellular mechanical interactions. Our approaches include stochastic simulations, the subcellular element method, and reaction-diffusion equations. Building upon this foundation, we have developed a deep learning-based dynamical model using unbalanced dynamic optimal transport to connect time-course single-cell transcriptomic snapshots and interrogate underlying gene regulatory networks. Lastly, we will discuss AI models designed to expedite protein design that incorporate a persistent spectralLaplacian method, large language models, and a hierarchical clustering-based Bayesian optimization approach.

Jan 25, 2024, 4:00 AM - 5:00 PM PT 

Dr. Daniel Gomez (University of California, Irvine)

Title: Asymptotic Analysis of Localized and Singular Perturbations with Lévy Flights

Abstract: How long will a confined Brownian particle take to hit an exceedingly small target? It is a classical result that the expected value of this first hitting time (FHT) blows up as the size of the target vanishes in two or more spatial dimensions. This is an example of a "strongly localized perturbation" in the sense that small geometric defects have large global effects. If Brownian motion is replaced with Lévy flights, a spatially discontinuous jump process, then the FHT has the potential to blow up even in the case of one spatial dimension. In this talk, I will discuss how matched asymptotic expansions yield a computationally inexpensive method for computing the FHT in the case of Lévy flights by reducing the problem to that of solving a linear system of equations. Moreover, we will see that depending on the fractional order of the Lévy flight, the FHT is qualitatively similar to that for Brownian motion in one or more spatial dimensions. In addition to analyzing FHT problems, matched asymptotic expansions have also been highly successful in studying localized solutions to singularly perturbed reaction diffusion systems. I will conclude by outlining how matched asymptotic expansions similarly yield nonlinear algebraic systems, globally coupled eigenvalue problems, and differential algebraic equations that describe the structure and dynamical properties of localized solutions.

Feb 7, 2024, 4:00 PM - 5:00 PM PT 

Dr. Chi-Wang Shu (Brown University)

Title: Stability of Time Discretizations for Semi-discrete High Order Schemes for Time-dependent PDEs

Abstract: In scientific and engineering computing, we encounter time-dependent partial differential equations (PDEs) frequently. When designing high order schemes for solving these time-dependent PDEs, we often first develop semi-discrete schemes paying attention only to spatial discretizations and leaving time t continuous. It is then important to have a high order time discretization to main the stability properties of the semi-discrete schemes. In this talk we discuss several classes of high order time discretization, including the strong stability preserving (SSP) time discretization, which preserves strong stability from a stable spatial discretization with Euler forward, the implicit-explicit (IMEX) Runge-Kutta or multi-step time marching, which treats the more stiff term (e.g. diffusion term in a convection-diffusion equation) implicitly and the less stiff term (e.g. the convection term in such an equation) explicitly, for which strong stability can be proved under the condition that the time step is upper-bounded by a constant under suitable conditions, the explicit-implicit-null (EIN) time marching, which adds a linear highest derivative term to both sides of the PDE and then uses IMEX time marching, and is particularly suitable for high order PDEs with leading nonlinear terms, and the explicit Runge-Kutta methods, for which strong stability can be proved in many cases for semi-negative linear semi-discrete schemes. Numerical examples will be given to demonstrate the performance of these schemes.

Feb 14, 2024, 10:00 AM - 11:00 AM PT 

Dr. Liu Yang (UCLA)

Title: Towards Large Scientific Learning Models with In-Context Operator Networks

Abstract: Can we build a single large model for a wide range of PDE-related scientific learning tasks? Can this model generalize to new PDEs, even of new forms, without any fine-tuning? We proposed in-context operator learning and the corresponding model In-Context Operator Networks (ICON) as an initial exploration of these questions. This approach draws inspiration from Large Language Models (LLMs), where the model performs a task specified by the prompted “context”, including task descriptions and a few related examples. We will show how a single ICON model manages 19 distinct equations/types of operators, encompassing forward and inverse ODEs, PDEs, and mean-field control problems, with each type containing infinitely many operators. Using 1D scalar nonlinear conservation laws as examples, we will show that ICON can generalize well to PDEs with new forms without any fine-tuning. We believe ICON represents a promising direction towards a large foundation model for scientific machine learning.

Reference: 

[1] In-Context Operator Learning with Data Prompts for Differential Equation Problems (https://www.pnas.org/doi/10.1073/pnas.2310142120)

[2] Fine-Tune Language Models as Multi-Modal Differential Equation Solvers (https://arxiv.org/pdf/2308.05061.pdf)

[3] PDE Generalization of In-Context Operator Networks: A Study on 1D Scalar Nonlinear Conservation Laws (https://arxiv.org/pdf/2401.07364.pdf) 

Feb 21, 2024, 1:00 PM - 1:50 PM PT 

Dr. Stacey Finley (USC)

Title: Exploring the tumor-immune ecosystem using computational modeling

Abstract: My research group works in the area of mathematical oncology, where we use mathematical models to decipher the complex networks of reactions inside of cancer cells and interactions between cells. We have combined detailed, mechanistic and data-driven modeling to study these networks and predict ways to control tumor growth. Our recent work is aimed at predicting metabolism and signaling in the tumor microenvironment. In this talk, I will present our recent work aimed at predicting signaling-mediated interactions between tumor and immune cells using agent-based models. Our models generate novel mechanistic insight into cell behavior and predict the effects of strategies aimed at inhibiting tumor growth. We have also developed methods of calibrating the models to tumor image data to generate reliable predictive frameworks.

Feb 28, 2024, 11:00 AM - 11:50 AM PT 

Dr. Max Hill (UC Riverside)

Title: An Introduction to Mathematical Phylogenetics: Algebraic and Probabilistic Perspectives in Modeling Biological Evolution

Abstract: In this talk I will introduce mathematical phylogenetics, a field of study motivated by the goal of recovering the evolutionary history of life on Earth. I will present a model of how nucleotides evolve between species related by a common ancestor. The emphasis of the talk will be showing how a few simple assumptions about nucleotide evolution can lead to a rich mathematical model, with both probabilistic and algebraic structure.