Krishna Kumar

krishnak@utexas.edu

About

Krishna Kumar is an Assistant Professor at the Civil, Architecture, and Environmental Engineering at the University of Texas at Austin. Krishna completed his Ph.D. from the University of Cambridge in January 2015 on multi-scale multiphase modeling of granular flows and was supervised by Professor Kenichi Soga. Krishna’s work involves developing exascale micro and macro-scale numerical methods: Material Point Method, Lattice Boltzmann - Discrete Element coupling, Finite Element Method, and Lattice Element method. His work in high-performance computing in geomechanics provides insights into the mechanics of natural hazards such as landslides. Krishna uses Machine Learning (ML) to model multi-scale problems in geomechanics. Krishna is a Software Sustainability Institute Fellow, UK, and has developed many open-source research codes. Krishna also builds large-scale graph networks and agent-based models for simulating the resilience of city-scale infrastructure systems.


Publications

GNS: A generalizable Graph Neural Network-based simulator for particulate and fluid modeling

Kumar, K., Vantassel, J.;

We develop a PyTorch-based Graph Network Simulator (GNS) that learns physics and predicts the flow behavior of particulate and fluid systems. GNS discretizes the domain with nodes representing a collection of material points and the links connecting the nodes representing the local interaction between particles or clusters of particles. The GNS learns the interaction laws through message passing on the graph. GNS has three components: (a) Encoder, which embeds particle information to a latent graph, the edges are learned functions; (b) Processor, which allows data propagation and computes the nodal interactions across steps; and (c) Decoder, which extracts the relevant dynamics (e.g., particle acceleration) from the graph. We introduce physics-inspired simple inductive biases, such as an inertial frame that allows learning algorithms to prioritize one solution (constant gravitational acceleration) over another, reducing learning time. The GNS implementation uses semi-implicit Euler integration to update the next state based on the predicted accelerations. GNS trained on trajectory data is generalizable to predict particle kinematics in complex boundary conditions not seen during training. The trained model accurately predicts within a 5% error of its associated material point method (MPM) simulation. The predictions are 5,000x faster than traditional MPM simulations (2.5 hours for MPM simulations versus 20 s for GNS simulation of granular flow). GNS surrogates are popular for solving optimization, control, critical-region prediction for in situ viz, and inverse-type problems. The GNS code is available under the open-source MIT license at https://github.com/geoelements/gns.

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Using explainability to design physics-aware CNNs for solving subsurface inverse problems

Crocker, J., Kumar, K., Cox, B.;

We present a novel method of using explainability techniques to design physics-aware neural networks. We demonstrate our approach by developing a convolutional neural network (CNN) for solving an inverse problem for shallow subsurface imaging. Although CNNs have gained popularity in recent years across many fields, the development of CNNs remains an art, as there are no clear guidelines regarding the selection of hyperparameters that will yield the best network. While optimization algorithms may be used to select hyperparameters automatically, these methods focus on developing networks with high predictive accuracy while disregarding model explainability (descriptive accuracy). However, the field of Explainable Artificial Intelligence (XAI) addresses the absence of model explainability by providing tools that allow developers to evaluate the internal logic of neural networks. In this study, we use the explainability methods Score-CAM and Deep SHAP to select hyperparameters, such as kernel sizes and network depth, to develop a physics-aware CNN for shallow subsurface imaging. We begin with a relatively deep Encoder-Decoder network, which uses surface wave dispersion images as inputs and generates 2D shear wave velocity subsurface images as outputs. Through model explanations, we ultimately find that a shallow CNN using two convolutional layers with an atypical kernel size of 3x1 yields comparable predictive accuracy but with increased descriptive accuracy. We also show that explainability methods can be used to evaluate the network’s complexity and decision-making. We believe this method can be used to develop neural networks with high predictive accuracy while also providing inherent explainability.

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Minority Report: A graph network oracle for in situ visualization

Kumar, K., Navratil, P., Solis, A., Vantassel, J;

In situ visualization techniques are hampered by a lack of foresight: crucial simulation phenomena can be missed due to a poor sampling rate or insufficient detail at critical timesteps. Keeping a human in the loop is impractical, and defining statistical triggers can be difficult. This paper demonstrates the potential for using a machine-learning-based simulation surrogate as an oracle to identify expected critical regions of a large-scale simulation. These critical regions are used to drive the in situ analysis, providing greater data fidelity and analysis resolution with an equivalent I/O budget to a traditional in situ framework. We develop a distributed asynchronous in situ visualization by integrating TACC Galaxy with CB-Geo MPM for material point simulation of granular flows. We employ a PyTorch-based 3D Graph Network Simulator (GNS) trained on granular flow problems as an oracle to predict the dynamics of granular flows. Critical regions of interests are manually tagged in GNS for in situ rendering in MPM.

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Hybrid Finite Element and Material Point Method to simulate granular column collapse from failure initiation to runout

Sordo, B., Rathje, E., Kumar, K.;

The performance evaluation of a potentially unstable slope involves two key components: the initiation of the slope failure and the post-failure runout. The Finite Element Method (FEM) excels at modeling the initiation of instability but quickly loses accuracy in modeling large-deformation problems due to mesh distortion. Hence, the FEM is unable to accurately model post-failure slope runout. Hybrid Eulerian-Lagrangian methods, such as the Material Point Method (MPM), offer a promising alternative for solving large-deformation problems, because particles can move freely across a background mesh, allowing for large deformation without computational issues. However, the use of moving material points in MPM for integration rather than the fixed Gauss points of the FEM reduces the accuracy of MPM in predicting stress distribution and thus failure initiation. We have created a hybrid method by initiating a failure simulation in FEM and subsequently transferring the coordinates, velocities, and stresses to MPM particles to model the runout behavior, combining the strength of both methods. We demonstrate the capability of the hybrid approach by simulating the collapse of a frictional granular column, comparing it to an empirical solution, and evaluating a suitable time to transfer from FEM to MPM by trialing multiple iterations with transfers at different stages of the collapse.

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A machine learning approach to predicting pore pressure response in liquefiable sands under cyclic loading

Choi, Y., Kumar, K.;

Shear stress history controls the pore pressure response in liquefiable soils. The excess pore pressure does not increase under cyclic loading when shear stress amplitude is lower than the peak prior amplitude – the shielding effect. Many sophisticated constitutive models fail to capture the shielding effect observed in the cyclic liquefaction experiments. We develop a data-driven machine learning model based on the LSTM neural network to capture the liquefaction response of soils under cyclic loading. The LSTM model is trained on 12 laboratory cyclic simple shear tests on Nevada sand in loose and dense conditions subjected to different cyclic simple shear loading conditions. The LSTM model features include the relative density of soil and the previous stress history to predict the pore water pressure response. The LSTM model successfully replicates the pore pressure response for three cyclic simple test results considering the shielding and density effects.

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Investigating the source of hysteresis in the Soil-Water Characteristic Curve using the multiphase lattice Boltzmann method

Hosseini, R., Kumar, K., Delenne, J.Y.;

The soil-water characteristic curve (SWCC) is the most fundamental relationship in unsaturated soil mechanics, relating the amount of water in the soil to the corresponding matric suction. From experimental evidence, it is known that SWCC exhibits hysteresis (i.e. wetting/drying path dependence). Various factors have been proposed as contributors to SWCC hysteresis, including air entrapment, contact angle hysteresis, ink-bottle effect, and change of soil fabric due to swelling and shrinkage, however, the significance of their contribution is debated. From our pore-scale numerical simulations, using the multiphase lattice Boltzmann method, we see that even when controlling for all these factors SWCC hysteresis still occurs, indicating that there is some underlying source that is not accounted for in these factors. We find this underlying source by comparing the liquid/gas phase distributions for simulated wetting and drying experiments of 2D and 3D granular packings. We see that during wetting (i.e. pore filling) many liquid bridges expand simultaneously and join together to fill the pores from the smallest to the largest, allowing menisci with larger radii of curvature (lower matric suction). Whereas, during drying (i.e. pore emptying), only the limited existing gas clusters can expand, which become constrained by the size of the pore openings surrounding them and result in menisci with smaller radii of curvature (higher matric suction).

Investigating the effect of porosity on the soil water retention curve using the multiphase Lattice Boltzmann Method

Hosseini, R., Kumar, K., Delenne, J.Y.;
Powders and Grains 2021, Buenos Aires, Argentina

The soil water retention curve (SWRC) is the most commonly used relationship in the study of unsaturated soil. In this paper, the effect of porosity on the SWRC is investigated by numerically modeling unsaturated soil using the Shan-Chen multiphase Lattice Boltzmann Method. The shape of simulated SWRCs are compared against that predicted by the van Genuchten model, demonstrating a good fit except at low degrees of saturation. The simulated SWRCs show an increase in the air-entry value as porosity decreases.

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Conductive and convective heat transfer in inductive heating of subsea buried pipelines

Kumar, K., El Mohtar, C., and Gilbert, R.;
ASCE Journal of Pipeline Systems Engineering and Practice

Inductive heating with high-voltage cables reduces the risk of hydrate formation by raising the temperature of the production fluid in pipelines. Heating the pipeline results in losing a certain fraction of the heat to the surrounding soil through conduction or convection-dominated flow through the soil. However, the amount of heat lost in conduction versus convection and the transition from conduction to convection-dominated heat loss remains unknown. Soil permeability, temperature gradient between cable and mudline, and burial depth influence the mode of heat transfer and the amount of heat lost. We study the dominant mode of heat transfer in pipelines with inductive heating using 2D Finite Difference analysis under different soil and environmental conditions. Low permeability soils primarily exhibit conductive heat transfer, thus losing minimum heat to the surrounding soil. In contrast, convective flow drives a significant fraction of the heat away from the pipeline and towards the ground surface for highly permeable soils, barely heating the fluid in the pipe. We identify a critical Rayleigh-Darcy number of 1 as the controlling value separating conduction and convection-dominated heat transfer. An increase in burial depth deteriorates the heating efficiency in convection-dominated high permeability soils, while it remains unaffected in conduction-dominated low permeability soils.

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In-situ visualization of natural hazards with Galaxy and Material Point Method

Abram, G., Solis, A., Liang, Y., and Kumar, K.;
IEEE Computing in Science & Engineering

Visualizing regional-scale landslides is the key to conveying the threat of natural hazards to stakeholders and policymakers. Traditional visualization techniques are restricted to post-processing a limited subset of simulation data and are not scalable to rendering exascale models with billions of particles. In-situ visualization is a technique of rendering simulation data in real-time, i.e., rendering visuals in tandem while the simulation is running. In this study, we develop a scalable N:M interface architecture to visualize regional-scale landslides. We demonstrate the scalability of the architecture by simulating the long runout of the 2014 Oso landslide using the Material Point Method coupled with the Galaxy ray tracing engine rendering 4.2 million material points as spheres. In-situ visualization has an amortized runtime increase of 2\% compared to non-visualized simulations. The developed approach can achieve in-situ visualization of regional-scale landslides with billions of particles with minimal impact on the simulation process.

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Effect Of Slope Angle On The Runout Evolution of Granular Column Collapse for Varying Initial Volumes

Wang, Q., Hosseini, R., Kumar, K.;
Proceedings of the 20th International Conference on Soil Mechanics and Geotechnical Engineering, Sydney 2021

In nature, submarine slope failures usually carry thousands of cubic-meters of sediments across extremely long distances and cause tsunamis and damages to offshore structures. This paper uses the granular column collapse experiment to investigate the effect of slope angle on the runout behavior of submarine granular landslides for different initial volumes. A two-dimensional coupled lattice Boltzman and discrete element method (LBM-DEM) approach is adopted for numerically modeling the granular column collapse. Columns with four different slope angles and six different volumes are modelled under both dry and submerged conditions. The effects of hydrodynamic interactions, including the generation of excess pore pressures, hydroplaning, and drag forces and formation of turbulent vortices, are used to explain the difference in the runout behavior of the submerged columns compared to the dry columns. The results show that at any given slope angle, there is a threshold volume above which the submerged columns have a larger final runout compared to their dry counterpart, and this threshold volume decreases with slope angle.

Effect of Initial Volume on the Run-Out Behavior of Submerged Granular Columns

Wang, Q., Hosseini, R., Kumar, K.;
GeoCongress 2021, Dallas, USA

Submarine landslides transport thousands of cubic meters of sediment across continental shelves even at slopes as low as 1° and can cause significant casualty and damage to infrastructure. The run-out mechanism in a submarine landslide is affected by factors such as the initial packing density, permeability, slope angle, and initial volume. While past studies have focused on the influence of density, permeability, and slope angle on the granular column collapse, the impact of volume on the run-out characteristics has not been investigated. This study aims to understand how the initial volume affects the run-out using a two-dimensional coupled lattice Boltzman and discrete element (LBM-DEM) method. The coupled LBM-DEM approach allows simulating fluid flow at the pore-scale resolution to understand the grain-scale mechanisms driving the complex continuum-scale response in the granular column collapse. For submerged granular column collapse, the run-out mechanism is heavily influenced by the interaction between the grains and the surrounding fluid. The development of negative pore pressures during shearing and hydrodynamic drag forces inhibit the flow. On the other hand, entrainment of water resulting in hydroplaning enhances the flow. With an increase in volume, the interaction between the grains and the surrounding fluid varies, causing changes in the run-out behavior. For smaller volumes, the forces inhibiting the underwater flow predominates, resulting in shorter run-outs than their dry counterparts. At large volumes, hydroplaning results in larger run-out than the dry cases, despite the inhibiting effects of drag forces and negative pore pressures.

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Power electronics packaging for in-road wireless charging installations

Ridge, A., Konaklieva, S., Bradley, S., McMahon, R. A., Kumar, K.;
IEEE Workshop on Emerging Technologies - Wireless Power (WoW), San Diego, USA, 1-4 June 2021

When power electronics are deployed under the road surface as part of a wireless system it is important to know that their packaging provides adequate heat extraction as well as the required environmental protection – often conflicting requirements. Presently very little can be found in wireless charging standards and literature on the topic of thermal modelling for in-ground components. Yet, this is a topic of great practical significance especially for in-road systems. Traditional cooling methods are not readily applicable underground. This paper uses finite element thermal modelling to investigate the cooling of a representative medium-power in-road wireless system, housed in a sealed ground assembly (GA) chamber and installed to UK requirements (HAUC). The paper quantitatively compares design options and provides practical recommendations for in-road installation thermal management.

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Biomechanical trade‑offs in the pelvic floor constrain the evolution of the human birth canal

Stansfield, E.; Kumar, K.; Mitteroecker, P.; Grunstra, N. D. S.;
Proceedings of the National Academy of Sciences of the United States of America (PNAS)

Compared to most other primates, humans are characterized by a tight fit between the maternal birth canal and the fetal head, leading to a relatively high risk of neonatal and maternal mortality and morbidities. Obstetric selection is thought to favor a spacious birth canal, whereas the source for opposing selection is frequently assumed to relate to bipedal locomotion. An alternative, yet under-investigated, hypothesis is that a more expansive birth canal suspends the soft tissue of the pelvic floor across a larger area, which is disadvantageous for continence and support of the weight of the inner organs and fetus. To test this “pelvic floor hypothesis” we generated a finite element model of the human female pelvic floor and varied its radial size and thickness while keeping all else constant. This allowed us to study the effect of pelvic geometry on pelvic floor deflection (i.e., the amount of bending from the original position) and tissue stresses and stretches. Deflection grew disproportionately fast with increasing radial size, and stresses and stretches also increased. By contrast, an increase in thickness increased pelvic floor stiffness - i.e. the resistance to deformation - which reduced deflection but was unable to fully compensate for the effect of increasing radial size. Moreover, larger thicknesses increase the intra-abdominal pressure necessary for childbirth. Our results support the pelvic floor hypothesis and evince functional trade-offs affecting not only the size of the birth canal but also the thickness and stiffness of the pelvic floor.

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Using Convolutional Neural Networks (CNN) to develop starting models for 2D full waveform inversion

Vantassel, J. P.; Kumar, K.; Cox, B. R.;
Geophysics

Non-invasive subsurface imaging using full waveform inversion (FWI) has the potential to fundamen-tally change engineering site characterization by enabling the recovery of high resolution 2D/3D maps ofsubsurface stiffness. Yet, the accuracy of FWI remains quite sensitive to the choice of the initial start-ing model due to the complexity and non-uniqueness of the inverse problem. In response, we presentthe novel application of convolutional neural networks (CNNs) to transform an experimental seismicwavefield acquired using a linear array of surface sensors directly into a robust starting model for 2DFWI. We begin by describing three key steps used for developing the CNN, which include: selectionof a network architecture, development of a suitable training set, and performance of network training.The ability of the trained CNN to predict a suitable starting model for 2D FWI was compared againstother commonly used starting models for a classic near-surface imaging problem; the identification of anundulating, two-layer, soil-bedrock interface. The CNN developed during this study was able to predictcomplex 2D subsurface images of the testing set directly from their seismic wavefields with an averagemean absolute percent error of 6%. When compared to other common approaches, the CNN approachwas able to produce starting models with smaller seismic image and waveform misfits, both before andafter FWI. The ability of the CNN to generalize to subsurface models which were dissimilar to the onesupon which it was trained was assessed using a more complex, three-layered model. While the predictiveability of the CNN was slightly reduced, it was still able to achieve seismic image and waveform misfitscomparable to the other commonly used starting models. This study demonstrates that CNNs have greatpotential as a tool for developing good starting models for FWI, which are critical for producing accurateFWI results.

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Investigating the thixotropic behaviour of tremie concrete using the slump‑flow test and the Material Point Method

Wilkes, C.; Kumar, K.; Biscontin, G.;
Concrete Rheology

A new thixotropic model is developed integrating the Papanastasiou-Bingham model with thixotropy equations to simulate the flow behaviour of Tremie Concrete in the Material Point Method framework. The effect of thixotropy on the rheological behaviour of fresh concrete is investigated by comparing field measurements with numerical simulations. The comparison yields new insights into a critical and often overlooked behaviour of concrete. A parametric study is performed to understand the effect of model parameters and rest-time on the shear stress response of fresh concrete. The Material Point Method with the Papanastasiou-Bingham model reproduces slump-flow measurements observed in the field. The novel model revealed a decline in concrete workability during the Slump-flow test after a period of rest due to thixotropy, which the physical version of the test fails to capture. This reduction in workability significantly affects the flow behaviour and the effective use of fresh concrete in construction operation.

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