Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics

Ji, Weiqi; Qiu, Weilun; Shi, Zhiyu; Pan, Shaowu; Deng, Sili

doi:10.1021/acs.jpca.1c05102

Cited by 150 publications

(85 citation statements)

References 47 publications

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“…Utilizing ML techniques in this model will allow for a much more efficient and automated predictive model for determining NP biodistribution. However, it is necessary to construct an informative PBPK compartmental model to ultimately use in the training process of this Neural Network [25], [26].…”

Section: Discussionmentioning

confidence: 99%

“…Our system being a stiff one makes it ideal for testing the performance of a new method and comparing it against highly optimized ODE solvers. It has been shown [26] that neural networks can be used to solve ODEs when the system of ODEs is nonstiff. We used QSSA to make our PBPK model nonstiff (stiffness ratio ∼ 10 4 ) and trained a neural network to learn the solution to the ODEs.…”

Section: Neural Network To Solve Odesmentioning

confidence: 99%

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Physiologically Based Multiphysics Pharmacokinetic Model for Determining the Temporal Biodistribution of Targeted Nanoparticles

Glass

Kulkarni

Eng

et al. 2022

Preprint

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Nanoparticles (NP) are being increasingly explored as vehicles for targeted drug delivery because they can overcome free therapeutic limitations by drug encapsulation, thereby increasing solubility and transport across cell membranes. However, a translational gap exists from animal to human studies resulting in only several NP having FDA approval. Because of this, researchers have begun to turn toward physiologically based pharmacokinetic (PBPK) models to guide in vivo NP experimentation. However, typical PBPK models use an empirically derived framework that cannot be universally applied to varying NP constructs and experimental settings. The purpose of this study was to develop a physics-based multiscale PBPK compartmental model for determining continuous NP biodistribution. We successfully developed two versions of a physics-based compartmental model, models A and B, and validated the models with experimental data. The more physiologically relevant model (model B) had an output that more closely resembled experimental data as determined by normalized root mean squared deviation (NRMSD) analysis. A branched model was developed to enable the model to account for varying NP sizes. With the help of the branched model, we were able to show that branching in vasculature causes enhanced uptake of NP in the organ tissue. The models were solved using two of the most popular computational platforms, MATLAB and Julia. Our experimentation with the two suggests the highly optimized ODE solver package DifferentialEquations.jl in Julia outperforms MATLAB when solving a stiff system of ordinary differential equations (\textbf{ODEs}). We experimented with solving our PBPK model with a neural network using Julia's Flux.jl package. We were able to demonstrate that a neural network can learn to solve a system of ODEs when the system can be made non-stiff via quasi-steady-state approximation (QSSA). In the future, this model will incorporate modules that account for varying NP surface chemistries, multiscale vascular hydrodynamic effects, and effects of the immune system to create a more comprehensive and modular model for predicting NP biodistribution in a variety of NP constructs.

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Section: Discussionmentioning

confidence: 99%

Section: Neural Network To Solve Odesmentioning

confidence: 99%

Physiologically Based Multiphysics Pharmacokinetic Model for Determining the Temporal Biodistribution of Targeted Nanoparticles

Glass

Kulkarni

Eng

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Recently developed differential combustion simulation packages, like Arrhenius.jl [59], could seamlessly integrate existing gas-phase kinetic models with CRNN models to predict combustion behaviors and backpropagate the error to the pyrolysis submodels. In addition, with the development of physics-informed neural networks [60,61], one can also learn the pyrolysis sub-models from experimental data with flow-chemistry interactions characterized by partial differential equations.…”

Section: Practical and Future Applications Of The Proposed Methodologymentioning

confidence: 99%

Autonomous kinetic modeling of biomass pyrolysis using chemical reaction neural networks

Ji¹,

Richter²,

Gollner³

et al. 2022

Combustion and Flame

Self Cite

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“…PINNs are trained to solve supervised learning tasks constrained by PDEs, such as the conservation laws in continuum theories of fluid and solid mechanics 16 , 22 – 24 . In addition to fluid and solid mechanism, PINNs have been used to solve a big amount of applications governed by differential equations such as radioactive transfer 25 , 26 , gas dynamics 27 , 28 , water dynamics 29 , Euler equation 30 , 31 , numerical integration 32 , chemical kinetics 33 , 34 and optimal control 35 , 36 .…”

Section: Introductionmentioning

confidence: 99%

Physics-informed attention-based neural network for hyperbolic partial differential equations: application to the Buckley–Leverett problem

Rodriguez-Torrado

Ruiz²,

Cueto‐Felgueroso

et al. 2022

Sci Rep

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Physics-informed neural networks (PINNs) have enabled significant improvements in modelling physical processes described by partial differential equations (PDEs) and are in principle capable of modeling a large variety of differential equations. PINNs are based on simple architectures, and learn the behavior of complex physical systems by optimizing the network parameters to minimize the residual of the underlying PDE. Current network architectures share some of the limitations of classical numerical discretization schemes when applied to non-linear differential equations in continuum mechanics. A paradigmatic example is the solution of hyperbolic conservation laws that develop highly localized nonlinear shock waves. Learning solutions of PDEs with dominant hyperbolic character is a challenge for current PINN approaches, which rely, like most grid-based numerical schemes, on adding artificial dissipation. Here, we address the fundamental question of which network architectures are best suited to learn the complex behavior of non-linear PDEs. We focus on network architecture rather than on residual regularization. Our new methodology, called physics-informed attention-based neural networks (PIANNs), is a combination of recurrent neural networks and attention mechanisms. The attention mechanism adapts the behavior of the deep neural network to the non-linear features of the solution, and break the current limitations of PINNs. We find that PIANNs effectively capture the shock front in a hyperbolic model problem, and are capable of providing high-quality solutions inside the convex hull of the training set.

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Stiff-PINN: Physics-Informed Neural Network for Stiff Chemical Kinetics

Cited by 150 publications

References 47 publications

Physiologically Based Multiphysics Pharmacokinetic Model for Determining the Temporal Biodistribution of Targeted Nanoparticles

Physiologically Based Multiphysics Pharmacokinetic Model for Determining the Temporal Biodistribution of Targeted Nanoparticles

Autonomous kinetic modeling of biomass pyrolysis using chemical reaction neural networks

Physics-informed attention-based neural network for hyperbolic partial differential equations: application to the Buckley–Leverett problem

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