Physics-based Machine Learning Research Articles

Statistical parameterized physics-based machine learning digital shadow models for laser powder bed fusion process

This paper presents a statistical physics-based machine learning model for predicting defects, such as surface roughness and lack-of-fusion porosity, in the laser powder bed fusion of metals (PBF-LB/M) additive manufacturing process. The statistical physics-based model is calibrated and validated against controlled single-track experiments and used for statistical prediction for multi-layer and multi-track cases for PBF-LB/M defects. A mechanistic reduced-order-based stochastic calibration process is introduced to capture the stochastic nature of the melt pool. The calibrated physics-based digital shadow model is demonstrated for predicting the surface roughness of the National Institute of Standards and Technology (NIST) overhang part X4, with a difference of 9.3% compared to the experimental results. By leveraging data obtained from both the physics-based model and experiments, a machine learning model has been trained for fast predictions (inference time of 0.4 ms) with high accuracy (error bound of 6.7%). This model can predict melt pool geometries under various processing conditions, offering a control strategy for the PBF-LB/M process. Further, the trained machine learning model is showcased to demonstrate a control application of melt pool geometries (width and depth) for specific processing parameters. These developed models (physics-based and machine learning) serve as a digital shadow of the PBF-LB/M process, offering predictive capabilities to build a digital twin model for process control, optimization, and online monitoring.

A physics based machine learning model to characterize room temperature semiconductor detectors in 3D

Room temperature semiconductor radiation detectors (RTSD) for X-ray and γ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\gamma$$\\end{document}-ray detection are vital tools for medical imaging, astrophysics and other applications. CdZnTe (CZT) has been the main RTSD for more than three decades with desired detection properties. In a typical pixelated configuration, CZT have electrodes on opposite ends. For advanced event reconstruction algorithms at sub-pixel level, detailed characterization of the RTSD is required in three dimensional (3D) space. However, 3D characterization of the material defects and charge transport properties in the sub-pixel regime is a labor intensive process with skilled manpower and novel experimental setups. Presently, state-of-art characterization is done over the bulk of the RTSD considering homogenous properties. In this paper, we propose a novel physics based machine learning (PBML) model to characterize the RTSD over a discretized sub-pixelated 3D volume which is assumed. Our novel approach is the first to characterize a full 3D charge transport model of the RTSD. In this work, we first discretize the RTSD between a pixelated electrodes spatially into 3 dimensions—x, y, and z. The resulting discretizations are termed as voxels in 3D space. In each voxel, the different physics based charge transport properties such as drift, trapping, detrapping and recombination of charges are modeled as trainable model weights. The drift of the charges considers second order non-linear motion which is observed in practice with the RTSDs. Based on the electron–hole pair injections as input to the PBML model, and signals at the electrodes, free and trapped charges (electrons and holes) as outputs of the model, the PBML model determines the trainable weights by backpropagating the loss function. The trained weights of the model represents one-to-one relation to that of the actual physical charge transport properties in a voxelized detector.

Condition Monitoring of Spud in Cutter Suction Dredger using Physics based Machine Learning

Condition Monitoring of Spud in Cutter Suction Dredger using Physics based Machine Learning

XLB: A differentiable massively parallel lattice Boltzmann library in Python

The lattice Boltzmann method (LBM) has emerged as a prominent technique for solving fluid dynamics problems due to its algorithmic potential for computational scalability. We introduce XLB library, a Python-based differentiable LBM library based on the JAX platform. The architecture of XLB is predicated upon ensuring accessibility, extensibility, and computational performance, enabling scaling effectively across CPU, TPU, multi-GPU, and distributed multi-GPU or TPU systems. The library can be readily augmented with novel boundary conditions, collision models, or multi-physics simulation capabilities. XLB's differentiability and data structure is compatible with the extensive JAX-based machine learning ecosystem, enabling it to address physics-based machine learning, optimization, and inverse problems. XLB has been successfully scaled to handle simulations with billions of cells, achieving giga-scale lattice updates per second. XLB is released under the permissive Apache-2.0 license and is available on GitHub at https://github.com/Autodesk/XLB. Program summaryProgram Title: XLBCPC Library link to program files:https://doi.org/10.17632/n25h65vw59.1Developer's repository link:https://github.com/Autodesk/XLBLicensing provisions: Apache-2.0Programming language: PythonNature of problem: XLB is a scalable Lattice Boltzmann simulation library based on JAX. It is designed to be accessible, extensible, and high performance. The library can be readily augmented with novel boundary conditions, collision models, or simulation capabilities. Moreover, XLB is differentiable, offering the unique advantage of integration with JAX's extensive machine learning ecosystem, and tackling physics-based machine learning, optimization, and inverse problems.Solution method: XLB utilizes the JAX library for just-in-time (JIT) compilation and distributed computing, enabling it to scale effectively across distributed multi-GPU/multi-TPU systems. XLB's programming model combines an object-oriented interface for easy extensibility. The library can be readily augmented with novel boundary conditions, collision models, or other simulation capabilities.

Trajectory Statistical Learning of the Potential Mean of Force and Diffusion Coefficient from Molecular Dynamics Simulations.

Central to studying the conformational changes of a complex protein is understanding the dynamics and energetics involved. Phenomenologically, structural dynamics can be formulated using an overdamped Langevin model along an observable, e.g., the distance between two residues in the protein. The Langevin model is specified by the deterministic force (the potential of mean force, PMF) and stochastic force (characterized by the diffusion coefficient, D). It is therefore of great interest to be able to extract both PMF and D from an observable time series but under the same computational framework. Here, we approach this challenge in molecular dynamics (MD) simulations by treating it as a missing-data Bayesian estimation problem. An important distinction in our methodology is that the entire MD trajectory, as opposed to the individual data elements, is used as the statistical variable in Bayesian imputation. This idea is implemented through an eigen-decomposition procedure for a time-symmetrized Fokker-Planck equation, followed by maximizing the likelihood for parameter estimation. The mathematical expressions for the functional derivatives used in learning PMF and D also provide new physical insights for the manner by which the information on both the deterministic and stochastic forces is encoded in the dynamics data. An all-atom MD simulation of a nontrivial biomolecule case is used to illustrate the application of this approach. We show that, interestingly, the results of trajectory statistical learning can motivate new order parameters for an improved description of the kinetic bottlenecks in conformational changes. Complementing purely data-driven or black-box methods, this work underscores the advantages of physics-based machine learning in gaining chemical insights from quantitative parameter estimation.

Perspectives of physics-based machine learning strategies for geoscientific applications governed by partial differential equations

Abstract. An accurate assessment of the physical states of the Earth system is an essential component of many scientific, societal, and economical considerations. These assessments are becoming an increasingly challenging computational task since we aim to resolve models with high resolutions in space and time, to consider complex coupled partial differential equations, and to estimate uncertainties, which often requires many realizations. Machine learning methods are becoming a very popular method for the construction of surrogate models to address these computational issues. However, they also face major challenges in producing explainable, scalable, interpretable, and robust models. In this paper, we evaluate the perspectives of geoscience applications of physics-based machine learning, which combines physics-based and data-driven methods to overcome the limitations of each approach taken alone. Through three designated examples (from the fields of geothermal energy, geodynamics, and hydrology), we show that the non-intrusive reduced-basis method as a physics-based machine learning approach is able to produce highly precise surrogate models that are explainable, scalable, interpretable, and robust.

Predicting meltpool depth and primary dendritic arm spacing in laser powder bed fusion additive manufacturing using physics-based machine learning

The long-term goal of this work is to predict and control the microstructure evolution in metal additive manufacturing processes. In pursuit of this goal, we developed and applied an approach which combines physics-based thermal modeling with machine learning to predict two important microstructure-related characteristics, namely, the meltpool depth and primary dendritic arm spacing in Nickel Alloy 718 parts made using the laser powder bed fusion (LPBF) process. Microstructure characteristics are critical determinants of functional physical properties, e.g., yield strength and fatigue life. Currently, the microstructure of LPBF parts is optimized through a cumbersome build-and-characterize empirical approach. Rapid and accurate models for predicting microstructure evolution are therefore valuable to reduce process development time and achieve consistent properties. However, owing to their computational complexity, existing physics-based models for predicting the microstructure evolution are limited to a few layers, and are challenging to scale to practical parts. This paper addresses the aforementioned research gap via a novel physics and data integrated modeling approach. The approach consists of two steps. First, a rapid, part-level computational thermal model was used to predict the temperature distribution and cooling rate in the entire part before it was printed. Second, the foregoing physics-based thermal history quantifiers were used as inputs to a simple machine learning model (support vector machine) trained to predict the meltpool depth and primary dendritic arm spacing based on empirical materials characterization data. As an example of its efficacy, when tested on a separate set of samples from a different build, the approach predicted the primary dendritic arm spacing with root mean squared error ≈ 110 nm. This work thus presents an avenue for future physics-based optimization and control of microstructure evolution in LPBF.

On the integration of Physics-Based Machine Learning with hierarchical Bayesian modeling techniques

Machine Learning (ML) has widely been used for modeling and predicting physical systems. These techniques offer high expressive power and good generalizability for interpolation within observed data sets. However, the disadvantage of black-box models is that they underperform under blind conditions since no physical knowledge is incorporated. Physics-based ML aims to address this problem by retaining the mathematical flexibility of ML techniques while incorporating physics. In accord, this paper proposes to embed mechanics-based models into the mean function of a Gaussian Process (GP) model and characterize potential discrepancies through kernel machines. A specific class of kernel function is promoted, which has a connection with the gradient of the physics-based model with respect to the input and parameters and shares similarity with the exact Auto-covariance function of linear dynamical systems. The spectral properties of the kernel function enable considering dominant periodic processes originating from physics misspecification. Nevertheless, the stationarity of the kernel function is a difficult hurdle in the sequential processing of long data sets, resolved through hierarchical Bayesian techniques. This implementation is also advantageous to mitigate computational costs, alleviating the scalability of GPs when dealing with sequential data. Using numerical and experimental examples, potential applications of the proposed method to structural dynamics inverse problems are demonstrated.

Atomic masses with machine learning for the astrophysical r process

The astrophysical r process plays a vital role in the production of heavy elements. Modeling of the r process is sensitive to masses and further requires knowledge of masses beyond current experimental reach. Therefore, simulations of the r process offer a unique test bed for predicting mass extrapolations. We take a Machine-Learning (ML) approach to model the masses across the entire chart of nuclides. For the first time, we simulate r-process nucleosynthesis with a physics-based ML mass model. We compare simulated abundances to solar data in order to evaluate the model's performance far from stability. The resulting r-process abundances up to thorium and uranium qualitatively match those of the observed solar system abundance pattern, with the characteristic peaks well positioned. We propagate the mass uncertainties obtained from the ML model to r-process abundance yields to estimate an uncertainty band associated with our approach. The size of the uncertainty band is approximately one order of magnitude which aligns with the uncertainty reported using alternative techniques.

Modeling for free dendrite growth based on physically-informed machine learning method

In order to overcome limitations of traditional theoretical and numerical models, based on machine learning (ML) method, three models were developed for dendrite growth in undercooled alloy melts to predict solid-liquid interfacial velocity, including purely data-driven model-1, model-2 based on Galenko-Danilov (GD) model and model-3 coupled with an extended GD model newly proposed by introducing thermo-kinetic correlation. A thoroughly comparative analysis was carried out by applying the three ML models to existing data of five alloys. Results verify that model-3 has the relatively better fitting ability to experimental data in case of interpolation, due to the varied effective kinetic coefficient introduced and the thermo-kinetic correlation considered. Both cases of complete and partial extrapolations were discussed. It is concluded that on the whole the two physics-based ML models, especially model-3, are superior to the purely data-driven ML model for extrapolation ability. Thus, ML model-3 is finally proposed in modeling dendrite growth.

Universal adaptive optics for microscopy through embedded neural network control

The resolution and contrast of microscope imaging is often affected by aberrations introduced by imperfect optical systems and inhomogeneous refractive structures in specimens. Adaptive optics (AO) compensates these aberrations and restores diffraction limited performance. A wide range of AO solutions have been introduced, often tailored to a specific microscope type or application. Until now, a universal AO solution – one that can be readily transferred between microscope modalities – has not been deployed. We propose versatile and fast aberration correction using a physics-based machine learning assisted wavefront-sensorless AO control (MLAO) method. Unlike previous ML methods, we used a specially constructed neural network (NN) architecture, designed using physical understanding of the general microscope image formation, that was embedded in the control loop of different microscope systems. The approach means that not only is the resulting NN orders of magnitude simpler than previous NN methods, but the concept is translatable across microscope modalities. We demonstrated the method on a two-photon, a three-photon and a widefield three-dimensional (3D) structured illumination microscope. Results showed that the method outperformed commonly-used modal-based sensorless AO methods. We also showed that our ML-based method was robust in a range of challenging imaging conditions, such as 3D sample structures, specimen motion, low signal to noise ratio and activity-induced fluorescence fluctuations. Moreover, as the bespoke architecture encapsulated physical understanding of the imaging process, the internal NN configuration was no-longer a “black box”, but provided physical insights on internal workings, which could influence future designs.

Integrating multi-source data to assess land subsidence sensitivity and management policies

Uneven land subsidence will cause damage to urban buildings and infrastructure and pose risks to human production and life. This study proposes a new methodology for factor identification and prediction of urban land subsidence that integrates physics-driven models and data-driven models. The driving factor layer was generated using multi-source datasets, and a comprehensive factor identification system was implemented. The machine learning method was used to calculate the comprehensive weight of each driving factor, and the identification and evaluation model of the land subsidence factor in Heze City was established. Then, the SARIMA model and the MODFLOW model were used to predict the development trend of the main influencing factors of land subsidence. Finally, the development trend of land subsidence was evaluated based on the physics-based machine learning model. The results show that the maximum average annual subsidence rate from 2016 to 2020 deduced by InSAR is 130.22 mm/yr, and the subsidence area accounts for 85.09%. It is estimated that the maximum annual average rate of land subsidence will be 65.14 mm/yr by 2025, and the subsidence area will account for 92.56%. The development degree of land subsidence has a significant relationship with groundwater exploitation and coal mining planning. By 2025, the proportion of areas with unchanged sensitivity levels will be 61.39%, and the prevention and control plan can be effectively implemented in most areas. The research provides a new methodology for evaluating the effectiveness of government planning policies and promoting scientific prevention and control.

Deep learning combined with singular value decomposition to reconstruct databases in fluid dynamics

Fluid dynamics problems are characterized by being multidimensional and nonlinear. Therefore, experiments and numerical simulations are complex and time-consuming. Motivated by this, the need arises to find new techniques to obtain data in a simpler way and in less time. In this article, we present a novel methodology based on physical principles to reconstruct databases with three, four and five dimensions, from sparse databases formed by sensor measurements. The methodology consists of combining Single Value Decomposition (SVD), which can extract the main flow dynamics, with neural networks. The neural network used is characterized by a simple architecture based on combining two autoencoders that work in parallel and are joined in the last layer. This new algorithm has been proved with three databases with different dimensions and complexities: in an Atmospheric Boundary Layer (ABL) with a turbulence model and in the flow past a two- and a three-dimensional cylinder. By applying this methodology, it has been achieved to reconstruct databases of different dimensions obtaining errors of the same order as those obtained in simulations. Summarizing, this work proposes a new hybrid physics-based machine learning model with a simple, robust and generalizable architecture, which allows reconstructing databases from very few sensors and with a very low computational cost.

Quality assessment and lifetime prediction of base metal electrode multilayer ceramic capacitors: Challenges and opportunities

Base metal electrode (BME) multilayer ceramic capacitors (MLCCs) are widely used in aerospace, medical, military, and communication applications, emphasizing the need for high reliability. The ongoing advancements in BaTiO3-based MLCC technology have facilitated further miniaturization and improved capacitive volumetric density for both low and high voltage devices. However, concerns persist regarding infant mortality failures and long-term reliability under higher fields and temperatures. To address these concerns, a comprehensive understanding of the mechanisms underlying insulation resistance degradation is crucial. Furthermore, there is a need to develop effective screening procedures during MLCC production and improve the accuracy of mean time to failure (MTTF) predictions. This article reviews our findings on the effect of the burn-in test, a common quality control process, on the dynamics of oxygen vacancies within BME MLCCs. These findings reveal the burn-in test has a negative impact on the lifetime and reliability of BME MLCCS. Moreover, the limitations of existing lifetime prediction models for BME MLCCs are discussed, emphasizing the need for improved MTTF predictions by employing a physics-based machine learning model to overcome the existing models’ limitations. The article also discusses the new physical-based machine learning model that has been developed. While data limitations remain a challenge, the physics-based machine learning approach offers promising results for MTTF prediction in MLCCs, contributing to improved lifetime predictions. Furthermore, the article acknowledges the limitations of relying solely on MTTF to predict MLCCs’ lifetime and emphasizes the importance of developing comprehensive prediction models that predict the entire distribution of failures.

A physics-based machine learning technique rapidly reconstructs the wall-shear stress and pressure fields in coronary arteries.

With the global rise of cardiovascular disease including atherosclerosis, there is a high demand for accurate diagnostic tools that can be used during a short consultation. In view of pathology, abnormal blood flow patterns have been demonstrated to be strong predictors of atherosclerotic lesion incidence, location, progression, and rupture. Prediction of patient-specific blood flow patterns can hence enable fast clinical diagnosis. However, the current state of art for the technique is by employing 3D-imaging-based Computational Fluid Dynamics (CFD). The high computational cost renders these methods impractical. In this work, we present a novel method to expedite the reconstruction of 3D pressure and shear stress fields using a combination of a reduced-order CFD modelling technique together with non-linear regression tools from the Machine Learning (ML) paradigm. Specifically, we develop a proof-of-concept automated pipeline that uses randomised perturbations of an atherosclerotic pig coronary artery to produce a large dataset of unique mesh geometries with variable blood flow. A total of 1,407 geometries were generated from seven reference arteries and were used to simulate blood flow using the CFD solver Abaqus. This CFD dataset was then post-processed using the mesh-domain common-base Proper Orthogonal Decomposition (cPOD) method to obtain Eigen functions and principal coefficients, the latter of which is a product of the individual mesh flow solutions with the POD Eigenvectors. Being a data-reduction method, the POD enables the data to be represented using only the ten most significant modes, which captures cumulatively greater than 95% of variance of flow features due to mesh variations. Next, the node coordinate data of the meshes were embedded in a two-dimensional coordinate system using the t-distributed Stochastic Neighbor Embedding (-SNE) algorithm. The reduced dataset for -SNE coordinates and corresponding vector of POD coefficients were then used to train a Random Forest Regressor (RFR) model. The same methodology was applied to both the volumetric pressure solution and the wall shear stress. The predicted pattern of blood pressure, and shear stress in unseen arterial geometries were compared with the ground truth CFD solutions on "unseen" meshes. The new method was able to reliably reproduce the 3D coronary artery haemodynamics in less than 10 s.

Instantaneous detection of acute myocardial infarction and ischaemia from a single carotid pressure waveform in rats.

Myocardial infarction (MI) is one of the leading causes of death worldwide. It is well accepted that early diagnosis followed by early reperfusion therapy significantly increases the MI survival. Diagnosis of acute MI is traditionally based on the presence of chest pain and electrocardiogram (ECG) criteria. However, around 50% of the MIs are without chest pain, and ECG is neither completely specific nor definitive. Therefore, there is an unmet need for methods that allow detection of acute MI or ischaemia without using ECG. Our hypothesis is that a hybrid physics-based machine learning (ML) method can detect the occurrence of acute MI or ischaemia from a single carotid pressure waveform. We used a standard occlusion/reperfusion rat model. Physics-based ML classifiers were developed using intrinsic frequency parameters extracted from carotid pressure waveforms. ML models were trained, validated, and generalized using data from 32 rats. The final ML models were tested on an external stratified blind dataset from additional 13 rats. When tested on blind data, the best ML model showed specificity = 0.92 and sensitivity = 0.92 for detecting acute MI. The best model's specificity and sensitivity for ischaemia detection were 0.85 and 0.92, respectively. We demonstrated that a hybrid physics-based ML approach can detect the occurrence of acute MI and ischaemia from carotid pressure waveform in rats. Since carotid pressure waveforms can be measured non-invasively, this proof-of-concept pre-clinical study can potentially be expanded in future studies for non-invasive detection of MI or myocardial ischaemia.

Development of a hydrate risk assessment tool based on machine learning for CO2 storage in depleted gas reservoirs

Depleted gas reservoirs are attractive sites for Carbon Capture and Storage (CCS) due to their huge storage capacities, proven seal integrity, existing infrastructure and subsurface data availability. However, CO2 injection into depleted formations can potentially lead to hydrate formation near the wellbore due to Joule-Thomson cooling, which might cause injectivity issues. Some challenges encountered when modeling and simulating this process are the computational time caused by Newton’s convergence issues and instability. The objective of this work is to propose a novel approach for hydrate risk assessment during CO2 injection into depleted gas reservoirs using physics-based Machine Learning (ML) approach. First, the selection of input parameters for the ML models is performed based on sensitivity study results using an analytical solution for different operational and petrophysical values. Then the ML models are tuned and tested using datasets from numerical reservoir simulation results based on a wide range of input parameter values. To the best of our knowledge, this is the first time that an ML approach is used for risk assessment of CO2 hydrate in its storage in depleted gas reservoirs. The ML models developed in this study presented an efficient performance to predict hydrate-forming events. The deep neural network model performed best with a 95% recall value and 84% precision value. These results show that the ML model can be further utilized for risk assessment in the screening stage, and the combination of screening by ML, followed by detailed analysis with numerical simulation in high-risk cases can be an efficient probing workflow for future CCS projects.

Recent Advances and Applications of Machine Learning in Experimental Solid Mechanics: A Review

AbstractFor many decades, experimental solid mechanics has played a crucial role in characterizing and understanding the mechanical properties of natural and novel artificial materials. Recent advances in machine learning (ML) provide new opportunities for the field, including experimental design, data analysis, uncertainty quantification, and inverse problems. As the number of papers published in recent years in this emerging field is growing exponentially, it is timely to conduct a comprehensive and up-to-date review of recent ML applications in experimental solid mechanics. Here, we first provide an overview of common ML algorithms and terminologies that are pertinent to this review, with emphasis placed on physics-informed and physics-based ML methods. Then, we provide thorough coverage of recent ML applications in traditional and emerging areas of experimental mechanics, including fracture mechanics, biomechanics, nano- and micromechanics, architected materials, and two-dimensional materials. Finally, we highlight some current challenges of applying ML to multimodality and multifidelity experimental datasets, quantifying the uncertainty of ML predictions, and proposing several future research directions. This review aims to provide valuable insights into the use of ML methods and a variety of examples for researchers in solid mechanics to integrate into their experiments.

Improved prediction for failure time of multilayer ceramic capacitors (MLCCs): A physics-based machine learning approach

Multilayer ceramic capacitors (MLCC) play a vital role in electronic systems, and their reliability is of critical importance. The ongoing advancement in MLCC manufacturing has improved capacitive volumetric density for both low and high voltage devices; however, concerns about long-term stability under higher fields and temperatures are always a concern, which impact their reliability and lifespan. Consequently, predicting the mean time to failure (MTTF) for MLCCs remains a challenge due to the limitations of existing models. In this study, we develop a physics-based machine learning approach using the eXtreme Gradient Boosting method to predict the MTTF of X7R MLCCs under various temperature and voltage conditions. We employ a transfer learning framework to improve prediction accuracy for test conditions with limited data and to provide predictions for test conditions where no experimental data exists. We compare our model with the conventional Eyring model (EM) and, more recently, the tipping point model (TPM) in terms of accuracy and performance. Our results show that the machine learning model consistently outperforms both the EM and TPM, demonstrating superior accuracy and stability across different conditions. Our model also exhibits a reliable performance for untested voltage and temperature conditions, making it a promising approach for predicting MTTF in MLCCs.

Machine learning quantum-chemical bond scission in thermosets under extreme deformation

Despite growing interest in polymers under extreme conditions, most atomistic molecular dynamics simulations cannot describe the bond scission events underlying failure modes in polymer networks undergoing large strains. In this work, we propose a physics-based machine learning approach that can detect and perform bond breaking with near quantum-chemical accuracy on-the-fly in atomistic simulations. Particularly, we demonstrate that by coarse-graining highly correlated neighboring bonds, the prediction accuracy can be dramatically improved. By comparing with existing quantum mechanics/molecular mechanics methods, our approach is approximately two orders of magnitude more efficient and exhibits improved sensitivity toward rare bond breaking events at low strain. The proposed bond breaking molecular dynamics scheme enables fast and accurate modeling of strain hardening and material failure in polymer networks and can accelerate the design of polymeric materials under extreme conditions.