PDE & Applied math seminar
Wednesday 1-1:50 pm, https://ucr.zoom.us/j/172617506
Organizers : Weitao Chen / Heyrim Cho / Yat Tin Chow / Qixuan Wang
Past Organizers : Mark Alber / James Kelliher / Amir Moradifam
Wednesday 1-1:50 pm, https://ucr.zoom.us/j/172617506
Organizers : Weitao Chen / Heyrim Cho / Yat Tin Chow / Qixuan Wang
Past Organizers : Mark Alber / James Kelliher / Amir Moradifam
Spring 2020 Schedule
Apr 01 13:00 (Wed) Organizing Meeting
Apr 07 11:00 (Tue) Dr. William Cannon (PNNL), joint with ICQMB center seminar
Apr 15 13:00 (Wed) Dr. Jasper Weinburd (Harvey Mudd College) (Cho)
Apr 22 13:00 (Wed) Dr. Youngjoon Hong (SDSU) (Chen)
Apr 29 13:00 (Wed) Dr. Adrian Lam (OSU)(QW)
May 06 13:00 (Wed) Dr. Qi Chen (UCR) (Chen), joint with ICQMB center seminar
May 12 11:00 (Tue) Dr. Kit Curtius (Cancer Research UK Barts Centre) (Cho), joint with ICQMB
May 20 13:00 (Wed) Dr. Xiu Yang (Lehigh University) (Cho)
June 03 13:00 (Wed) Dr. Seungjoon Lee (Johns Hopkins University) (Cho)
June 10 13:00 (Wed) Dr. Huan Lei (Michigan State University) (Cho) -> next quarter!
Title and Abstrcts
June 03 13:00 (Wed), 2020 (online)
Dr. Seungjoon Lee (Johns Hopkins University)
Title: Understanding Complex Systems from Heterogeneous Data via Machine Learning
Abstract: In the age of big data, recent developments in efficient measurement/simulation capabilities enable us to collect extensive data sets from heterogeneous sources across the different levels of fidelity, accuracy, scale, and resolution. Yet, understanding the spatiotemporal dynamic behavior of the complex system directly from data has been lagging behind due to the requirement of prior knowledge/intuition about the system. Modern data-driven approaches via machine learning suggest alternative ways to understand the underlying system directly from heterogeneous data. In this talk, I present such data-driven frameworks (1) to effectively combine heterogeneous data (e.g. multi-fidelity data); (2) to extract salient coarse-scale variables from fine-scale data; (3) to identify the corresponding coarse-scale governing equations (e.g. Partial Differential Equations or PDEs); (4) to control the complex system at the coarse-level under the uncertainties. Specifically, I employ machine learning (here Gaussian Processes) with/without data-driven embedding to combine multi-fidelity data. After that, I extract salient coarse-scale observables (e.g. concentration) from fine-scale data and discover the underlying coarse-scale PDEs using manifold learning (Diffusion Maps) and machine learning (Gaussian Processes and Artificial Neural Networks). I will demonstrate the effectiveness of the proposed data-driven frameworks through various examples in fluid dynamics, computational biology, dynamical system, and control. Moreover, I will present future work about the optimal design and control of the complex system under the uncertainties using the coarse-scale data-driven framework.
May 20 13:00 (Wed), 2020, (online)
Dr. Xiu Yang (Department of Industrial and System Engineering, Lehigh University)
Title: Embedding Physical Constraints in Learning Models
Abstract: Gaussian process (GP) regression is a widely used method in machine learning for classification, supervised learning, etc. The standard GP regression is a data driven method that uses observations (e.g., measurements) of a state of interest to construct a GP that describe the state. In many scientific and engineering problems, existing knowledge are available in the form of physical laws, governing equations, etc., that reflect (partial) understanding of the system. I will introduce two frameworks that incorporate these knowledge in a GP model. The first one uses state-of-the-art simulation tools in specific domain to constrct a GP that satisfies constraints in the form of equations, e.g., Dirichlet boundary condition, divergence-free flow field, conservation law. The other one is a data-driven method that imposes constraints in the form of inequalities, e.g., positivity preserving, with high probability.
May 12 11:00 (Tue), 2020, (online)
Dr. Kit Curtius (Barts Cancer Institute, Queen Mary University of London)
Title: Catching cancer in the act: biologically-based models to optimize screening and surveillance
Abstract: Effective screening is the cornerstone of most cancer early detection strategies. Nevertheless, in general screening strategies have led to minimal reduction in mortality, high cost to healthcare services, and paradoxically cause both under-diagnosis due to inadequate or insensitive screening and overdiagnosis due to ineffective patient stratification in surveillance protocols.
Here, I will illustrate how the efficacy of cancer screening can be improved by incorporating biologically-based multiscale models into the design of early detection strategies. As a case study in Barrett’s esophagus (BE) screening, we applied our methods for a stochastic model of progression to esophageal adenocarcinoma (EAC) that was previously calibrated to US cancer registry data. The model predicts optimal screening ages for patients with symptomatic gastroesophageal reflux disease to be older (58 for men, 64 for women) than what is currently recommended (age > 50 years). These ages are in a cost-effective range to start screening and were independently validated by data used in current guidelines. Our study demonstrates how mathematical modeling of cancer evolution can be used to optimize screening regimes, assess potential risks, and quantify associated costs. Surveillance regimes could also be improved if they were based on these models.
May 06 13:00 (Wed), 2020, (online)
Dr. Qi Chen (Division of Biomedical Sciences, School of Medicine, UCR)
Title: On the origin of mammalian early embryo symmetry-breaking
Abstract: In mammalian preimplantation embryo development, when the first asymmetry emerges and how it develops to direct distinct cell fates are two longstanding questions. It remains debatable whether the first bifurcation of cell fate emerges randomly at morula stage, or has been predetermined at earlier stages before morphological distinction. Combining single-cell RNA-seq analysis and mathematical modeling, we recently showed that the very first symmetry-breaking process involves both chance separation and defined transcriptional circuits. From our single-embryo transcriptome analysis, small biases at molecular level will inevitably emerge at the 2-cell embryo stage, following a binomial distribution due to the cleavage division. At this stage, the blastomere-to-blastomere distribution seems random but during subsequent zygotic transcriptional activation, a “bistable pattern” emerges in some genes. Several lineage specifiers show a strong bias between different blastomeres thus providing potential for further increased asymmetry subsequently. These observations suggest a scenario of how order is created from a seemingly random process through the differential triggering of existing master regulators by the emergence of their small bias. Recently, we also proposed that compartmentalized intracellular reactions, such as those mediated by cell-cell contact and cell geometry, generate micro-scale inhomogeneity, which is amplified in the developing embryo, driving pattern formation. Ongoing research in my lab strive to address these hypotheses.
Apr 29 13:00 (Wed), 2020, (online)
Dr. King-Yeung (Adrian) Lam (Ohio State University)
Title: PDEs in Evolution of Dispersal
Abstract: Beginning with the work of Alan Hastings in 1983, PDE models have played a major role in the study of evolution of dispersal. In this talk, I will discuss two classes of PDE models that comes from evolution of dispersal. In the first part, I will discuss existence/non-existence of evolutionarily stable strategies (ESS) in two-species competition models, which is motivated by the adaptive dynamics approach. In the second part, I will introduce a new class of models that describes a population structured by a quantitative trait, which describes the competition of an infinite number of species in a certain sense. We show the convergence to ESS in these models of a quantitative trait, and explain how that is connected to the aforementioned adaptive dynamics framework. This talk contains projects in collaboration with R.S. Cantrell, C. Cosner, W. Hao, B. Perthame, Y. Lou, and F. Lutscher.
Apr 22 13:00 (Wed), 2020, (online)
Dr. Youngjoon Hong (San Diego State University)
Title: Numerical Study of Nanoplasmonics and Solar Thermophotovoltaics
Abstract: The accurate simulation of scattering of electromagnetic waves in three dimensions by a diffraction grating is crucial in many applications of engineering and scientific interest. In this lecture, we explore a novel High-Order Perturbation of Surfaces method for the numerical approximation of electromagnetic scattering by a periodic layered medium. For this we apply the method of Transformed Field Expansions which delivers a Fourier collocation, Legendre-Galerkin, Boundary Perturbation approach to solve the problem in transformed coordinates. A sequence of numerical simulations demonstrate the efficient and robust spectral convergence which can be achieved with the proposed algorithm. As an application, our approaches can be generalized to investigate periodic metal interface shapes in Solar thermophotovoltaics structures that tailor thermal emission using nanophotonic structures for increased solar energy conversion.
Apr 15 13:00 (Wed), 2020, (online)
Dr. Jasper Weinburd (Harvey Mudd College)
Title: Agent-based and PDE Models for Foraging Locust Swarms
Abstract: Locusts are devastating pests that aggregate in large swarms, destroying crops, pasture, and wild vegetation. The shape of a swarm is correlated with its other collective qualities including density, average speed, and how much food is left uneaten. But each insect is governed by individual behaviors, primarily social interaction with other locusts and attraction to nearby food resources. In this talk, we’ll start to unravel the relationships between collective swarm qualities and individual insect behaviors. We’ll look in depth at two models: a set of partial differential equations (PDE) governing the mean-field density of locusts, and an agent-based model (ABM) that tracks the behavior of each locust. Traveling wave solutions in the PDE characterize collective swarming, feeding, and marching observable in the ABM. By examining 4.4 million parameter combinations, we identify biologically consistent parameters that reproduce field observations.
Apr 07 11:00 (Tue), 2020 (online)
Dr. William Cannon (PNNL)
Title: Combining Data, Control Theory, Statistical Thermodynamics with Machine Learning to Predict Enzyme Regulation, Metabolite Concentrations and Rate Constants
Abstract: Experimental measurement or computational inference/prediction of the enzyme regulation needed in a metabolic pathway is hard problem. Consequently, regulation is known only for well-studied reactions of central metabolism in a few organisms. In this study, we use statistical thermodynamics and metabolic control theory as a theoretical framework to determine the enzyme activities that are needed to control metabolite concentrations such that they are consistent with experimentally measured values. A reinforcement learning approach is utilized to learn optimal regulation policies that match physiological levels of metabolites while maximizing the entropy production rate and minimizing the heat loss. The learning takes a minimal amount of time, and efficient regulation schemes were learned that agree surprisingly well with known regulation. The learning is facilitated by a new approach in which steady state solutions are obtained by convex optimization rather than ODE solvers, making the time to solution seconds rather than days. The optimization is based on the Marcelin-De Donder formulation of mass action kinetics, from which rate constants are inferred. Consequently, a full ODE-based, mass action simulation with rate parameters and post-translational regulation is obtained. We demonstrate the process on three pathways in the central metabolism E. coli (gluconeogenesis, glycolysis-TCA, Pentose Phosphate-TCA) that each require different regulation schemes.