arXiv subjects

Souvik Chakraborty

Publications and source records attributed to Souvik Chakraborty.

At least 91 records · Page 5Linked to original sources

arXiv2023

Randomized prior wavelet neural operator for uncertainty quantification

In this paper, we propose a novel data-driven operator learning framework referred to as the \textit{Randomized Prior Wavelet Neural Operator} (RP-WNO). The proposed RP-WNO is an extension of the recently proposed wavelet neural operator, which boasts excellent generalizing capabilities but cannot estimate the uncertainty associated with its predictions. RP-WNO, unlike the vanilla WNO, comes with inherent uncertainty quantification module and hence, is expected to be extremely useful for scientists and engineers alike. RP-WNO utilizes randomized prior networks, which can account for prior information and is easier to implement for large, complex deep-learning architectures than its Bayesian counterpart. Four examples have been solved to test the proposed framework, and the results produced advocate favorably for the efficacy of the proposed framework.

stat.ML↗

arXiv2022

Probabilistic machine learning based predictive and interpretable digital twin for dynamical systems

A framework for creating and updating digital twins for dynamical systems from a library of physics-based functions is proposed. The sparse Bayesian machine learning is used to update and derive an interpretable expression for the digital twin. Two approaches for updating the digital twin are proposed. The first approach makes use of both the input and output information from a dynamical system, whereas the second approach utilizes output-only observations to update the digital twin. Both methods use a library of candidate functions representing certain physics to infer new perturbation terms in the existing digital twin model. In both cases, the resulting expressions of updated digital twins are identical, and in addition, the epistemic uncertainties are quantified. In the first approach, the regression problem is derived from a state-space model, whereas in the latter case, the output-only information is treated as a stochastic process. The concepts of Itô calculus and Kramers-Moyal expansion are being utilized to derive the regression equation. The performance of the proposed approaches is demonstrated using highly nonlinear dynamical systems such as the crack-degradation problem. Numerical results demonstrated in this paper almost exactly identify the correct perturbation terms along with their associated parameters in the dynamical system. The probabilistic nature of the proposed approach also helps in quantifying the uncertainties associated with updated models. The proposed approaches provide an exact and explainable description of the perturbations in digital twin models, which can be directly used for better cyber-physical integration, long-term future predictions, degradation monitoring, and model-agnostic control.

stat.ML↗

arXiv2022

MAntRA: A framework for model agnostic reliability analysis

We propose a novel model agnostic data-driven reliability analysis framework for time-dependent reliability analysis. The proposed approach -- referred to as MAntRA -- combines interpretable machine learning, Bayesian statistics, and identifying stochastic dynamic equation to evaluate reliability of stochastically-excited dynamical systems for which the governing physics is \textit{apriori} unknown. A two-stage approach is adopted: in the first stage, an efficient variational Bayesian equation discovery algorithm is developed to determine the governing physics of an underlying stochastic differential equation (SDE) from measured output data. The developed algorithm is efficient and accounts for epistemic uncertainty due to limited and noisy data, and aleatoric uncertainty because of environmental effect and external excitation. In the second stage, the discovered SDE is solved using a stochastic integration scheme and the probability failure is computed. The efficacy of the proposed approach is illustrated on three numerical examples. The results obtained indicate the possible application of the proposed approach for reliability analysis of in-situ and heritage structures from on-site measurements.

stat.ME↗

arXiv2022

Model-agnostic stochastic model predictive control

We propose a model-agnostic stochastic predictive control (MASMPC) algorithm for dynamical systems. The proposed approach first discovers \textit{interpretable} governing differential equations from data using a novel algorithm and blends it with a model predictive control algorithm. One salient feature of the proposed approach resides in the fact that it requires no input measurement (external excitation); the unknown excitation is instead treated as white noise, and a stochastic differential equation corresponding to the underlying system is identified. With the novel stochastic differential equation discovery framework, the proposed approach is able to generalize; this eliminates the repeated retraining phase -- a major bottleneck with other machine learning-based model agnostic control algorithms. Overall, the proposed MASMPC (a) is robust against measurement noise, (b) works with sparse measurements, (c) can tackle set-point changes, (d) works with multiple control variables, and (e) can incorporate dead time. We have obtained state-of-the-art results on several benchmark examples. Finally, we use the proposed approach for vibration mitigation of a 76-storey building under seismic loading.

eess.SY↗

arXiv2022

BYOLMed3D: Self-Supervised Representation Learning of Medical Videos using Gradient Accumulation Assisted 3D BYOL Framework

Applications on Medical Image Analysis suffer from acute shortage of large volume of data properly annotated by medical experts. Supervised Learning algorithms require a large volumes of balanced data to learn robust representations. Often supervised learning algorithms require various techniques to deal with imbalanced data. Self-supervised learning algorithms on the other hand are robust to imbalance in the data and are capable of learning robust representations. In this work, we train a 3D BYOL self-supervised model using gradient accumulation technique to deal with the large number of samples in a batch generally required in a self-supervised algorithm. To the best of our knowledge, this work is one of the first of its kind in this domain. We compare the results obtained through our experiments in the downstream task of ACL Tear Injury detection with the contemporary self-supervised pre-training methods and also with ResNet3D-18 initialized with the Kinetics-400 pre-trained weights. From the downstream task experiments, it is evident that the proposed framework outperforms the existing baselines.

cs.CV↗

arXiv2022

Evidence of a compensated semimetal with electronic correlations at the CNP of twisted double bilayer graphene

Recently, magic-angle twisted bilayer graphene (MATBLG) has shown the emergence of various interaction-driven novel quantum phases at the commensurate fillings of the moir'e superlattice, while the charge neutrality point (CNP) remains mostly a vanilla insulator. Here, we show an emerging phase of nearly compensated semimetallicity at the CNP of twisted double bilayer graphene (TDBLG), a close cousin of MATBLG, with signatures of electronic correlation. Using electrical and thermal transport, we find almost two orders of magnitude enhancement of the thermopower in magnetic fields much smaller than the extreme quantum limit, accompanied by a large magnetoresistance($\sim 2500\%$) at CNP. This provides indisputable experimental evidence that TDBLG near CNP is a compensated semimetal. Moreover, at low temperatures, we observe an unusual sublinear temperature dependence of resistance. A recent theory predicts the formation of an excitonic metal near CNP, where small electron and hole pockets coexist. We understand the sublinear temperature dependence in terms of critical fluctuations in this theory.

cond-mat.mes-hall↗

arXiv2022

Uncertainty Quantification and Sensitivity analysis for Digital Twin Enabling Technology: Application for BISON Fuel Performance Code

To understand the potential of intelligent confirmatory tools, the U.S. Nuclear Regulatory Committee (NRC) initiated a future-focused research project to assess the regulatory viability of machine learning (ML) and artificial intelligence (AI)-driven Digital Twins (DTs) for nuclear power applications. Advanced accident tolerant fuel (ATF) is one of the priority focus areas of the U.S. Department of Energy (DOE). A DT framework can offer game-changing yet practical and informed solutions to the complex problem of qualifying advanced ATFs. Considering the regulatory standpoint of the modeling and simulation (M&S) aspect of DT, uncertainty quantification and sensitivity analysis are paramount to the DT framework's success in terms of multi-criteria and risk-informed decision-making. This chapter introduces the ML-based uncertainty quantification and sensitivity analysis methods while exhibiting actual applications to the finite element-based nuclear fuel performance code BISON.

stat.AP↗

arXiv2022

Stochastic projection based approach for gradient free physics informed learning

We propose a stochastic projection-based gradient free physics-informed neural network. The proposed approach, referred to as the stochastic projection based physics informed neural network (SP-PINN), blends upscaled stochastic projection theory with the recently proposed physics-informed neural network. This results in a framework that is robust and can solve problems involving complex solution domain and discontinuities. SP-PINN is a gradient-free approach which addresses the computational bottleneck associated with automatic differentiation in conventional PINN. Efficacy of the proposed approach is illustrated by a number of examples involving regular domain, complex domain, complex response and phase field based fracture mechanics problems. Case studies by varying network architecture (activation function) and number of collocation points have also been presented.

cs.CE↗

arXiv2022

Deep Physics Corrector: A physics enhanced deep learning architecture for solving stochastic differential equations

We propose a novel gray-box modeling algorithm for physical systems governed by stochastic differential equations (SDE). The proposed approach, referred to as the Deep Physics Corrector (DPC), blends approximate physics represented in terms of SDE with deep neural network (DNN). The primary idea here is to exploit DNN to model the missing physics. We hypothesize that combining incomplete physics with data will make the model interpretable and allow better generalization. The primary bottleneck associated with training surrogate models for stochastic simulators is often associated with selecting the suitable loss function. Among the different loss functions available in the literature, we use the conditional maximum mean discrepancy (CMMD) loss function in DPC because of its proven performance. Overall, physics-data fusion and CMMD allow DPC to learn from sparse data. We illustrate the performance of the proposed DPC on four benchmark examples from the literature. The results obtained are highly accurate, indicating its possible application as a surrogate model for stochastic simulators.

stat.ML↗

arXiv2022

Learning governing physics from output only measurements

Extracting governing physics from data is a key challenge in many areas of science and technology. The existing techniques for equations discovery are dependent on both input and state measurements; however, in practice, we only have access to the output measurements only. We here propose a novel framework for learning governing physics of dynamical system from output only measurements; this essentially transfers the physics discovery problem from the deterministic to the stochastic domain. The proposed approach models the input as a stochastic process and blends concepts of stochastic calculus, sparse learning algorithms, and Bayesian statistics. In particular, we combine sparsity promoting spike and slab prior, Bayes law, and Euler Maruyama scheme to identify the governing physics from data. The resulting model is highly efficient and works with sparse, noisy, and incomplete output measurements. The efficacy and robustness of the proposed approach is illustrated on several numerical examples involving both complete and partial state measurements. The results obtained indicate the potential of the proposed approach in identifying governing physics from output only measurement.

physics.data-an↗

arXiv2022

Learning the Stress-Strain Fields in Digital Composites using Fourier Neural Operator

Increased demands for high-performance materials have led to advanced composite materials with complex hierarchical designs. However, designing a tailored material microstructure with targeted properties and performance is extremely challenging due to the innumerable design combinations and prohibitive computational costs for physics-based solvers. In this study, we employ a neural operator-based framework, namely Fourier neural operator (FNO) to learn the mechanical response of 2D composites. We show that the FNO exhibits high-fidelity predictions of the complete stress and strain tensor fields for geometrically complex composite microstructures with very few training data and purely based on the microstructure. The model also exhibits zero-shot generalization on unseen arbitrary geometries with high accuracy. Furthermore, the model exhibits zero-shot super-resolution capabilities by predicting high-resolution stress and strain fields directly from low-resolution input configurations. Finally, the model also provides high-accuracy predictions of equivalent measures for stress-strain fields allowing realistic upscaling of the results.

cond-mat.mtrl-sci↗

arXiv2022

Variational Bayes Deep Operator Network: A data-driven Bayesian solver for parametric differential equations

Neural network based data-driven operator learning schemes have shown tremendous potential in computational mechanics. DeepONet is one such neural network architecture which has gained widespread appreciation owing to its excellent prediction capabilities. Having said that, being set in a deterministic framework exposes DeepONet architecture to the risk of overfitting, poor generalization and in its unaltered form, it is incapable of quantifying the uncertainties associated with its predictions. We propose in this paper, a Variational Bayes DeepONet (VB-DeepONet) for operator learning, which can alleviate these limitations of DeepONet architecture to a great extent and give user additional information regarding the associated uncertainty at the prediction stage. The key idea behind neural networks set in Bayesian framework is that, the weights and bias of the neural network are treated as probability distributions instead of point estimates and, Bayesian inference is used to update their prior distribution. Now, to manage the computational cost associated with approximating the posterior distribution, the proposed VB-DeepONet uses \textit{variational inference}. Unlike Markov Chain Monte Carlo schemes, variational inference has the capacity to take into account high dimensional posterior distributions while keeping the associated computational cost low. Different examples covering mechanics problems like diffusion reaction, gravity pendulum, advection diffusion have been shown to illustrate the performance of the proposed VB-DeepONet and comparisons have also been drawn against DeepONet set in deterministic framework.

stat.ML↗

arXiv2022

Wavelet neural operator: a neural operator for parametric partial differential equations

With massive advancements in sensor technologies and Internet-of-things, we now have access to terabytes of historical data; however, there is a lack of clarity in how to best exploit the data to predict future events. One possible alternative in this context is to utilize operator learning algorithm that directly learn nonlinear mapping between two functional spaces; this facilitates real-time prediction of naturally arising complex evolutionary dynamics. In this work, we introduce a novel operator learning algorithm referred to as the Wavelet Neural Operator (WNO) that blends integral kernel with wavelet transformation. WNO harnesses the superiority of the wavelets in time-frequency localization of the functions and enables accurate tracking of patterns in spatial domain and effective learning of the functional mappings. Since the wavelets are localized in both time/space and frequency, WNO can provide high spatial and frequency resolution. This offers learning of the finer details of the parametric dependencies in the solution for complex problems. The efficacy and robustness of the proposed WNO are illustrated on a wide array of problems involving Burger's equation, Darcy flow, Navier-Stokes equation, Allen-Cahn equation, and Wave advection equation. Comparative study with respect to existing operator learning frameworks are presented. Finally, the proposed approach is used to build a digital twin capable of predicting Earth's air temperature based on available historical data.

physics.comp-ph↗

arXiv2022

Koopman operator for time-dependent reliability analysis

Time-dependent structural reliability analysis of nonlinear dynamical systems is non-trivial; subsequently, scope of most of the structural reliability analysis methods is limited to time-independent reliability analysis only. In this work, we propose a Koopman operator based approach for time-dependent reliability analysis of nonlinear dynamical systems. Since the Koopman representations can transform any nonlinear dynamical system into a linear dynamical system, the time evolution of dynamical systems can be obtained by Koopman operators seamlessly regardless of the nonlinear or chaotic behavior. Despite the fact that the Koopman theory has been in vogue a long time back, identifying intrinsic coordinates is a challenging task; to address this, we propose an end-to-end deep learning architecture that learns the Koopman observables and then use it for time marching the dynamical response. Unlike purely data-driven approaches, the proposed approach is robust even in the presence of uncertainties; this renders the proposed approach suitable for time-dependent reliability analysis. We propose two architectures; one suitable for time-dependent reliability analysis when the system is subjected to random initial condition and the other suitable when the underlying system have uncertainties in system parameters. The proposed approach is robust and generalizes to unseen environment (out-of-distribution prediction). Efficacy of the proposed approached is illustrated using three numerical examples. Results obtained indicate supremacy of the proposed approach as compared to purely data-driven auto-regressive neural network and long-short term memory network.

stat.ML↗

arXiv2022

Energy networks for state estimation with random sensors using sparse labels

State estimation is required whenever we deal with high-dimensional dynamical systems, as the complete measurement is often unavailable. It is key to gaining insight, performing control or optimizing design tasks. Most deep learning-based approaches require high-resolution labels and work with fixed sensor locations, thus being restrictive in their scope. Also, doing Proper orthogonal decomposition (POD) on sparse data is nontrivial. To tackle these problems, we propose a technique with an implicit optimization layer and a physics-based loss function that can learn from sparse labels. It works by minimizing the energy of the neural network prediction, enabling it to work with a varying number of sensors at different locations. Based on this technique we present two models for discrete and continuous prediction in space. We demonstrate the performance using two high-dimensional fluid problems of Burgers' equation and Flow Past Cylinder for discrete model and using Allen Cahn equation and Convection-diffusion equations for continuous model. We show the models are also robust to noise in measurements.

cs.LG↗

arXiv2022

Assessment of DeepONet for reliability analysis of stochastic nonlinear dynamical systems

Time dependent reliability analysis and uncertainty quantification of structural system subjected to stochastic forcing function is a challenging endeavour as it necessitates considerable computational time. We investigate the efficacy of recently proposed DeepONet in solving time dependent reliability analysis and uncertainty quantification of systems subjected to stochastic loading. Unlike conventional machine learning and deep learning algorithms, DeepONet learns is a operator network and learns a function to function mapping and hence, is ideally suited to propagate the uncertainty from the stochastic forcing function to the output responses. We use DeepONet to build a surrogate model for the dynamical system under consideration. Multiple case studies, involving both toy and benchmark problems, have been conducted to examine the efficacy of DeepONet in time dependent reliability analysis and uncertainty quantification of linear and nonlinear dynamical systems. Results obtained indicate that the DeepONet architecture is accurate as well as efficient. Moreover, DeepONet posses zero shot learning capabilities and hence, a trained model easily generalizes to unseen and new environment with no further training.

stat.ML↗

arXiv2022

Efficient hybrid topology optimization using GPU and homogenization based multigrid approach

We propose a new hybrid topology optimization algorithm based on multigrid approach that combines the parallelization strategy of CPU using OpenMP and heavily multithreading capabilities of modern Graphics Processing Units (GPU). In addition to that significant computational efficiency in memory requirement has been achieved using homogenization strategy. The algorithm has been integrated with versitile computing platform of MATLAB for ease of use and customization. The bottlenecking repetitive solution of the state equation has been solved using an optimized geometric multigrid approach along with CUDA parallelization enabling an order of magnitude faster in computational time than current state of the art implementations. On-the-fly computation of auxiliary matrices in the multigrid scheme and modification in interpolation schemes using homogenization strategy removes memory limitation of GPUs. Memory hierarchy of GPU has also been exploited for further optimized implementations. All these enable solution of structures involving hundred millions of three dimensional brick elements to be accomplished in a standard desktop computer or a workstation. Performance of the proposed algorithm is illustrated using several examples including design dependent loads and multimaterial.Results obtained indicate the excellent performance and scalability of the proposed approach.

cs.DC↗

arXiv2022

Deep Capsule Encoder-Decoder Network for Surrogate Modeling and Uncertainty Quantification

We propose a novel \textit{capsule} based deep encoder-decoder model for surrogate modeling and uncertainty quantification of systems in mechanics from sparse data. The proposed framework is developed by adapting Capsule Network (CapsNet) architecture into image-to-image regression encoder-decoder network. Specifically, the aim is to exploit the benefits of CapsNet over convolution neural network (CNN) $-$ retaining pose and position information related to an entity to name a few. The performance of proposed approach is illustrated by solving an elliptic stochastic partial differential equation (SPDE), which also governs systems in mechanics such as steady heat conduction, ground water flow or other diffusion processes, based uncertainty quantification problem with an input dimensionality of $1024$. However, the problem definition does not the restrict the random diffusion field to a particular covariance structure, and the more strenuous task of response prediction for an arbitrary diffusion field is solved. The obtained results from performance evaluation indicate that the proposed approach is accurate, efficient, and robust.

stat.ML↗