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DATA-DRIVEN AND PHYSICS INFORMED MODELLING OF CHINESE HAMSTER OVARY CELL BIOREACTORS

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arXiv 2023年

作者： Cui, Tianqi Bertalan, Tom S. Ndahiro, Nelson Khare, Pratik Betenbaugh, Michael Maranas, Costas Kevrekidis, Ioannis G. Department of Chemical and Biomolecular Engineering Johns Hopkins University BaltimoreMD21218 United States Department of Chemical Engineering The Pennsylvania State University University ParkPA16802 United States Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21218 United States

Fed-batch culture is an established operation mode for the production of biologics using mammalian cell cultures. Quantitative modeling integrates both kinetics for some key reaction steps and optimization-driven metabolic flux allocation, using flux balance analysis;this is known to lead to certain mathematical inconsistencies. Here, we propose a physically-informed data-driven hybrid model (a "gray box") to learn models of the dynamical evolution of Chinese Hamster Ovary (CHO) cell bioreactors from process data. The approach incorporates physical laws (e.g. mass balances) as well as kinetic expressions for metabolic fluxes. Machine learning (ML) is then used to (a) directly learn evolution equations (black-box modelling);(b) recover unknown physical parameters ("white-box" parameter fitting) or—importantly—(c) learn partially unknown kinetic expressions (gray-box modelling). We encode the convex optimization step of the overdetermined metabolic biophysical system as a differentiable, feed-forward layer into our architectures, connecting partial physical knowledge with data-driven machine learning. © 2023, CC BY.

关键词： Convex optimization

Integrable Fractional Modified Korteweg-de Vries, Sine-Gordon, and Sinh-Gordon Equations

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arXiv 2022年

作者： Ablowitz, Mark J. Been, Joel B. Carr, Lincoln D. Department of Applied Mathematics University of Colorado BoulderCO United States Department of Applied Mathematics and Statistics Department of Physics Colorado School of Mines GoldenCO United States Quantum Engineering Program Department of Applied Mathematics and Statistics Department of Physics Colorado School of Mines GoldenCO United States

The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations. Notably, this method can be extended to fractional nonlinear evolution equations characterized by anomalous dispersion using completeness of suitable eigenfunctions of the associated linear scattering problem. In anomalous diffusion, the mean squared displacement is proportional to tα, α > 0, while in anomalous dispersion, the speed of localized waves is proportional to Aα, where A is the amplitude of the wave. Fractional extensions of the modified Korteweg-deVries (mKdV), sine-Gordon (sineG) and sinh-Gordon (sinhG) and associated hierarchies are obtained. Using symmetries present in the linear scattering problem, these equations can be connected with a scalar family of nonlinear evolution equations of which fractional mKdV (fmKdV), fractional sineG (fsineG), and fractional sinhG (fsinhG) are special cases. Completeness of solutions to the scalar problem is obtained and, from this, the nonlinear evolution equation is characterized in terms of a spectral expansion. In particular, fmKdV, fsineG, and fsinhG are explicitly written. One-soliton solutions are derived for fmKdV and fsineG using the inverse scattering transform and these solitons are shown to exhibit anomalous dispersion. © 2022, CC BY.

关键词： Dispersion (waves)

Implementation and (Inverse Modified) Error Analysis for implicitly-templated ODE-nets

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arXiv 2023年

作者： Zhu, Aiqing Bertalan, Tom Zhu, Beibei Tang, Yifa Kevrekidis, Ioannis G. LSEC ICMSEC Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China Department of Chemical and Biomolecular Engineering Johns Hopkins University BaltimoreMD21211 United States School of Mathematics and Physics University of Science and Technology Beijing Beijing100083 China Department of Chemical and Biomolecular Engineering Department of Applied Mathematics and Statistics Johns Hopkins University BaltimoreMD21211 United States

We focus on learning unknown dynamics from data using ODE-nets templated on implicit numerical initial value problem solvers. First, we perform Inverse Modified error analysis of the ODE-nets using unrolled implicit schemes for ease of interpretation. It is shown that training an ODE-net using an unrolled implicit scheme returns a close approximation of an Inverse Modified Differential Equation (IMDE). In addition, we establish a theoretical basis for hyper-parameter selection when training such ODE-nets, whereas current strategies usually treat numerical integration of ODE-nets as a black box. We thus formulate an adaptive algorithm which monitors the level of error and adapts the number of (unrolled) implicit solution iterations during the training process, so that the error of the unrolled approximation is less than the current learning loss. This helps accelerate training, while maintaining accuracy. Several numerical experiments are performed to demonstrate the advantages of the proposed algorithm compared to nonadaptive unrollings, and validate the theoretical analysis. We also note that this approach naturally allows for incorporating partially known physical terms in the equations, giving rise to what is termed "gray box" identification. Copyright © 2023, The Authors. All rights reserved.

关键词： Error analysis

On The Mechanism of Nucleation in Pulsed-laser Quenched Si Films on SiO 2

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MRS Online Proceedings Library 2021年第1期1245卷 1-6页

作者： Y. Deng Q. Hu U. J. Chung A. M. Chitu A. B. Limanov S. James Im Program in Materials Science and Engineering Department of Applied Physics and Applied Mathematics Columbia University New York USA

We have investigated the solid nucleation mechanism in laser-quenched Si films on SiO2. Previously neglected experimental steps, consisting of BHF-etching and irradiation in vacuum, were implemented to reduce potential extrinsic influences. The resulting experimental findings and computational analysis lead us to conclude that solid nucleation consistently takes place heterogeneously at, and only at, the bottom liquid Si-SiO2 interface.

关键词： Si thin film nucleation & growth

Learning from 2D: machine learning of 3D effective properties of heterogeneous materials based on 2D microstructure sections

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arXiv 2023年

作者： Hu, Guangyu Latypov, Marat I. Department of Materials Science and Engineering University of Arizona TucsonAZ85721 United States Graduate Interdisciplinary Program in Applied Mathematics University of Arizona TucsonAZ85721 United States

Microstructure–property relationships are key to effective design of structural materials for advanced applications. Advances in computational methods enabled modeling microstructure-sensitive properties using 3D models (e.g., finite elements) based on microstructure representative volumes. 3D microstructure data required as input to these models are typically obtained from either 3D characterization experiments or digital reconstruction based on statistics from 2D microstructure images. In this work, we present machine learning (ML) approaches to modeling effective properties of heterogeneous materials directly from 2D microstructure sections. To this end, we consider statistical learning models based on spatial correlations and convolutional neural networks as two distinct ML strategies. In both strategies, models are trained on a dataset of synthetically generated 3D microstructures and their properties obtained from micromechanical 3D simulations. Upon training, the models predict properties from 2D microstructure sections. The advantage of the presented models is that they only need 2D sections, whose experimental acquisition is more accessible compared to 3D characterization. Furthermore, the present models do not require digital reconstruction of 3D microstructures. © 2023, CC BY.

关键词： Microstructure

Viscoelastic fluid flow in a slowly varying planar contraction: the role of finite extensibility on the pressure drop

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arXiv 2024年

作者： Mahapatra, Bimalendu Ruangkriengsin, Tachin Stone, Howard A. Boyko, Evgeniy Faculty of Mechanical Engineering Technion – Israel Institute of Technology Haifa3200003 Israel Program in Applied and Computational Mathematics Princeton University PrincetonNJ08544 United States Department of Mechanical and Aerospace Engineering Princeton University PrincetonNJ08544 United States

We analyze the steady viscoelastic fluid flow in slowly varying contracting channels of arbitrary shape and present a theory based on the lubrication approximation for calculating the flow rate–pressure drop relation at low and high Deborah (De) numbers. Unlike most prior theoretical studies leveraging the Oldroyd-B model, we describe the fluid viscoelasticity using a FENE-CR model and examine how the polymer chains’ finite extensibility impacts the pressure drop. We employ the low-Deborah-number lubrication analysis to provide analytical expressions for the pressure drop up to O(De4). We further consider the ultra-dilute limit and exploit a one-way coupling between the parabolic velocity and elastic stresses to calculate the pressure drop of the FENE-CR fluid for arbitrary values of the Deborah number. Such an approach allows us to elucidate elastic stress contributions governing the pressure drop variations and the effect of finite extensibility for all De. We validate our theoretical predictions with two-dimensional numerical simulations and find excellent agreement. We show that, at low Deborah numbers, the pressure drop of the FENE-CR fluid monotonically decreases with De, similar to the previous results for the Oldroyd-B and FENE-P fluids. However, at high Deborah numbers, in contrast to a linear decrease for the Oldroyd-B fluid, the pressure drop of the FENE-CR fluid exhibits a non-monotonic variation due to finite extensibility, first decreasing and then increasing with de. Nevertheless, even at sufficiently high Deborah numbers, the pressure drop of the FENE-CR fluid in the ultra-dilute and lubrication limits is lower than the corresponding Newtonian pressure drop. © 2024, CC BY.

关键词： Non Newtonian flow

Special Issue on Artificial Intelligence for Synthetic Biology

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ACS SYNTHETIC BIOLOGY 2024年第2期13卷 408-410页

作者： Martin, Hector Garcia Mazurenko, Stanislav Zhao, Huimin Biological Systems and Engineering Division Lawrence Berkeley National Laboratory Berkeley California 94720 United States BCAM − Basque Center for Applied Mathematics Bilbao 48009 Spain DOE Agile BioFoundry Emeryville California 94608 United States DOE Joint BioEnergy Institute Emeryville California 94608 United States Loschmidt Laboratories Department of Experimental Biology and RECETOX Faculty of Science Masaryk University Kamenice 5 625 00 Brno Czech Republic International Clinical Research Center St. Anne’s University Hospital Brno Pekarska 53 656 91 Brno Czech Republic Department of Chemical and Biomolecular Engineering University of Illinois at Urbana−Champaign Urbana Illinois 61801 United States

Viscosity Solutions of the Eikonal Equation on the Wasserstein Space∗

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arXiv 2023年

作者： Soner, H. Mete Yan, Qinxin Department of Operations Research and Financial Engineering Princeton University PrincetonNJ08540 United States Program in Applied and Computational Mathematics Princeton University PrincetonNJ08540 United States

Dynamic programming equations for mean field control problems with a separable structure are Eikonal type equations on the Wasserstein space. Standard differentiation using linear derivatives yield a direct extension of the classical viscosity theory. We use Fourier representation of the Sobolev norms on the space of measures, together with the standard techniques from the finite dimensional theory to prove a comparison result among semicontinuous sub and super solutions, obtaining a unique characterization of the value *** Codes 35D40, 35Q89, 49L12, 49L25, 60G99 © 2023, CC BY-NC-ND.

关键词： Viscosity

The effectiveness of distance learning through Edmodo and Video Conferencing Jitsi Meet

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The effectiveness of distance learning through Edmodo and Vi...

2020 National Physical Education Seminar, SNPF 2020

作者： Asfar, A.M.I.T. Asfar, A.M.I.A. Department of Mathematics Education STKIP Muhammadiyah Bone Indonesia Doctoral Program Science Education Universitas Negeri Makassar Indonesia Department of Chemical Engineering Politeknik Negeri Ujung Pandang Indonesia

Distance learning is intensively used since the outbreak of the Covid-19 requires the lecture to be done from home. A variety of applications to support distance learning, including e-learning Edmodo as a learning management system with video conference jits meet to optimize lectures online. The purpose of this study is to see the course's effectiveness by using e-learning Edmodo with or without a video conference Jitsi Meet in reducing students' mistakes in answering the questions given. Research design using experimental type posttest, only group control design. The object of research consists of two classes, namely class control and class comparison. The analysis results indicate the use of an e-learning Edmodo integrated video conference Jitsi Meet provides advantages compared to only using e-learning Edmodo because it can reduce the level of error in answering questions by 50%. © Published under licence by IOP Publishing Ltd.

关键词： Video conferencing