arXiv subjects

Krishna Kumar

Publications and source records attributed to Krishna Kumar.

At least 37 records · Page 2Linked to original sources

arXiv2025

Investigating the effect of CPT in lateral spreading prediction using Explainable AI

This study proposes an autoencoder approach to extract latent features from cone penetration test profiles to evaluate the potential of incorporating CPT data in an AI model. We employ autoencoders to compress 200 CPT profiles of soil behavior type index (Ic) and normalized cone resistance (qc1Ncs) into ten latent features while preserving critical information. We then utilize the extracted latent features with site parameters to train XGBoost models for predicting lateral spreading occurrences in the 2011 Christchurch earthquake. Models using the latent CPT features outperformed models with conventional CPT metrics or no CPT data, achieving over 83% accuracy. Explainable AI revealed the most crucial latent feature corresponding to soil behavior between 1-3 meter depths, highlighting this depth range's criticality for liquefaction evaluation. The autoencoder approach provides an automated technique for condensing CPT profiles into informative latent features for machine-learning liquefaction models.

cs.LG↗

arXiv2025

Runout of liquefaction-induced tailings dam failure: Influence of earthquake motions and residual strength

This study utilizes a hybrid Finite Element Method (FEM) and Material Point Method (MPM) to investigate the runout of liquefaction-induced flow slide failures. The key inputs to this analysis are the earthquake ground motion, which induces liquefaction, and the post-liquefaction residual strength. The influence of these factors on runout is evaluated by subjecting a model of a tailings dam to thirty different earthquake motions and by assigning different values of post-liquefaction residual strength. Ground motions with larger peak ground accelerations (PGA) generate liquefaction to larger depths, thus mobilizing a greater mass of material and resulting in a flow slide with greater runout. However, different ground motions with the same PGA yield significant variations in the depth of liquefaction, indicating that other ground motion characteristics (e.g., frequency content) also exert significant influence over the initiation of liquefaction. Ground motion characteristics of peak ground velocity (PGV) and Modified Acceleration Spectrum Intensity (MASI) show a strong correlation to the induced depth of liquefaction because they capture both the intensity and frequency content of the earthquake motion. The computed runout is directly related to the depth of liquefaction induced by the earthquake motion. For dam geometry analyzed, measurable runout occurs when liquefaction extends to 10 m depth and the runout is maximized when liquefaction extends to about 18 m. Strain-softening of the residual strength of the liquefied tailings during runout is shown to substantially increase the runout distance of the flow slide, highlighting the need for additional research to better characterize the appropriate strength of liquefied materials during flow failures.

physics.geo-ph↗

arXiv2024

Measuring the effective stress parameter using the multiphase lattice Boltzmann method and investigating the source of its hysteresis

The effective stress parameter, $χ$, is essential for calculating the effective stress in unsaturated soils. Experimental measurements have captured different relationships between $χ$ and the degree of saturation, $S_r$; however, they have not been able to justify the particular shapes of the $χ$-$S_r$ curves. Theoretical solutions express $χ$ as a function of $S_r$ and the air-water interfacial area, $a_{wn}$; however, $a_{wn}$ is difficult to predict, limiting further investigation of $χ$ variation. We seek an alternative approach for studying $χ$ by simulating the pore-scale distribution of the two fluid phases in unsaturated soils using the multiphase lattice Boltzmann method (LBM). We develop an algorithm for measuring $χ$ based on the suction and surface tension forces applied to each grain. Using this algorithm, we simulate the $χ$-$S_r$ curve over a full hydraulic cycle for a synthetic 3D granular soil column with immobile grains. We find that $χ=1$ at $S_r=1$ and $χ=0$ at $S_r=0$, while $χ>S_r$ for all other saturations. The maximum divergence of $χ$ from $S_r$ happens at the transition from/to the pendular regime. We also observe that the $χ$-$S_r$ curve is hysteretic; $χ$ is larger during wetting (imbibition) compared to drying (drainage) due to larger contribution of surface tension forces.

cond-mat.soft↗

arXiv2024

A hybrid Finite Element and Material Point Method for modeling liquefaction-induced tailings dam failures

This paper presents a hybrid Finite Element Method (FEM) and Material Point Method (MPM) approach for modeling liquefaction-induced tailings dam failures from initiation through runout. We apply this method to simulate the 1978 Mochikoshi tailings dam failure, which occurred due to seismic loading and liquefaction during an earthquake. Our approach leverages FEM to capture the initial failure mechanism and MPM to simulate the subsequent runout, exploiting the strength of each method in their respective phases of the failure process. We investigate the impact of the FEM-to-MPM transfer time on runout results, identifying an optimal transfer window. This window begins when liquefaction reaches a critical depth to fully trigger the failure and ends before excessive mesh deformation occurs. Our findings demonstrate that the properties of the liquefied tailings significantly influence runout predictions. Notably, we achieve runout distances comparable to the case history only when incorporating additional strain-softening beyond the initial liquefaction-induced strength reduction. Our results demonstrate that the hybrid FEM-MPM method effectively models tailings dam failures associated with complex failure mechanisms and large runouts. This approach offers a promising tool for predicting the runout of seismic liquefaction-induced tailings dam failures, improving risk assessment and mitigation strategies in tailings dam management.

physics.geo-ph↗

arXiv2024

Nuclear Dependence of Beam Normal Single Spin Asymmetry in Elastic Scattering from Nuclei

We propose to measure the beam normal single spin asymmetry in elastic scattering of transversely polarized electron from target nuclei with 12 $\leq Z \leq$ 90 at Q$^2$ = 0.0092 GeV$^2$ to study its nuclear dependence. While the theoretical calculations based on two-photon exchange suggest no nuclear dependence at this kinematics, the results of 208Pb from Jefferson Lab show a striking disagreement from both theoretical predictions and light nuclei measurements. The proposed measurements will provide new data for intermediate to heavy nuclei where no data exists for $Z \geq$ 20 in the kinematics of previous high-energy experiments. It will allow one to investigate the missing contributions that are not accounted in the current theoretical models.

nucl-ex↗

arXiv2024

Basis-to-Basis Operator Learning Using Function Encoders

We present Basis-to-Basis (B2B) operator learning, a novel approach for learning operators on Hilbert spaces of functions based on the foundational ideas of function encoders. We decompose the task of learning operators into two parts: learning sets of basis functions for both the input and output spaces and learning a potentially nonlinear mapping between the coefficients of the basis functions. B2B operator learning circumvents many challenges of prior works, such as requiring data to be at fixed locations, by leveraging classic techniques such as least squares to compute the coefficients. It is especially potent for linear operators, where we compute a mapping between bases as a single matrix transformation with a closed-form solution. Furthermore, with minimal modifications and using the deep theoretical connections between function encoders and functional analysis, we derive operator learning algorithms that are directly analogous to eigen-decomposition and singular value decomposition. We empirically validate B2B operator learning on seven benchmark operator learning tasks and show that it demonstrates a two-orders-of-magnitude improvement in accuracy over existing approaches on several benchmark tasks.

cs.LG↗

arXiv2024

Machine Learning Aided Modeling of Granular Materials: A Review

Artificial intelligence (AI) has become a buzz word since Google's AlphaGo beat a world champion in 2017. In the past five years, machine learning as a subset of the broader category of AI has obtained considerable attention in the research community of granular materials. This work offers a detailed review of the recent advances in machine learning-aided studies of granular materials from the particle-particle interaction at the grain level to the macroscopic simulations of granular flow. This work will start with the application of machine learning in the microscopic particle-particle interaction and associated contact models. Then, different neural networks for learning the constitutive behaviour of granular materials will be reviewed and compared. Finally, the macroscopic simulations of practical engineering or boundary value problems based on the combination of neural networks and numerical methods are discussed. We hope readers will have a clear idea of the development of machine learning-aided modelling of granular materials via this comprehensive review work.

physics.geo-ph↗

arXiv2024

Sequential hybrid finite element and material point method to simulate slope failures

Numerical modeling of slope failures seeks to predict two key phenomena: the initiation of failure and the post-failure runout. Currently, most modeling methods for slope failure analysis excel at one of these two but are deficient in the other. For example, the Finite Element Method (FEM) models the initiation of instability well but quickly loses accuracy when modeling large deformations because of mesh distortion, restricting its ability to predict runout. Conversely, the Material Point Method (MPM) utilizes material points which move freely across a background grid, allowing for indefinite deformations without computational issues. However, MPM is restricted in its ability to model slope failure initiation due to limitations of the available boundary conditions and reduced accuracy of its stress distributions. The sequential hybridization of these two methods, initiating a model in FEM and then transferring to MPM, presents an opportunity to accurately capture both initiation and runout by a single model. The exact time for this transfer is not self-apparent, but it must be conducted after the initiation mechanism and before excessive mesh distortion. By simulating two granular column failures and two slope failures, we demonstrate the effectiveness of this hybrid FEM-MPM method and identify the appropriate time to transfer.

math.NA↗

arXiv2024

Inverse analysis of granular flows using differentiable graph neural network simulator

Inverse problems in granular flows, such as landslides and debris flows, involve estimating material parameters or boundary conditions based on target runout profile. Traditional high-fidelity simulators for these inverse problems are computationally demanding, restricting the number of simulations possible. Additionally, their non-differentiable nature makes gradient-based optimization methods, known for their efficiency in high-dimensional problems, inapplicable. While machine learning-based surrogate models offer computational efficiency and differentiability, they often struggle to generalize beyond their training data due to their reliance on low-dimensional input-output mappings that fail to capture the complete physics of granular flows. We propose a novel differentiable graph neural network simulator (GNS) by combining reverse mode automatic differentiation of graph neural networks with gradient-based optimization for solving inverse problems. GNS learns the dynamics of granular flow by representing the system as a graph and predicts the evolution of the graph at the next time step, given the current state. The differentiable GNS shows optimization capabilities beyond the training data. We demonstrate the effectiveness of our method for inverse estimation across single and multi-parameter optimization problems, including evaluating material properties and boundary conditions for a target runout distance and designing baffle locations to limit a landslide runout. Our proposed differentiable GNS framework offers an orders of magnitude faster solution to these inverse problems than the conventional finite difference approach to gradient-based optimization.

physics.geo-ph↗

arXiv2024

Modeling liquefaction-induced runout of a tailings dam using a hybrid finite element and material point method approach

Tailings dams impound large amounts of saturated soil which can be highly susceptible to liquefaction. Liquefaction results in a severe loss of strength in the retained soil and potentially failure of the dam. If the dam is breached, a massive debris flow of liquefied soil is then released with potentially disastrous consequences downstream. Numerical models are frequently utilized to predict the liquefaction response of tailings dams and the potential runout, and these analyses inform engineering decisions regarding hazard avoidance and mitigation. The Finite Element Method (FEM) is a widespread tool which excels at modeling liquefaction triggering and initial movements, but it quickly loses accuracy when modeling large deformations due to mesh distortion. Conversely, the Material Point Method (MPM), a hybrid Eulerian-Lagrangian method, employs particles that move freely across a background grid and can account for large deformations without losing accuracy. However, issues with the accuracy of MPM's stress distributions and limits associated with the available boundary conditions impair its ability to predict liquefaction initiation. In this paper, we utilize a sequential hybridization of the FEM and MPM methods as a superior alternative to either individually. To demonstrate the efficacy of this hybrid method to simulate the entire process of tailings dam failures from initiation to runout, we model the 1978 Mochikoshi Tailings Dam failure.

physics.geo-ph↗

arXiv2024

Explainable AI models for predicting liquefaction-induced lateral spreading

Earthquake-induced liquefaction can cause substantial lateral spreading, posing threats to infrastructure. Machine learning (ML) can improve lateral spreading prediction models by capturing complex soil characteristics and site conditions. However, the "black box" nature of ML models can hinder their adoption in critical decision-making. This study addresses this limitation by using SHapley Additive exPlanations (SHAP) to interpret an eXtreme Gradient Boosting (XGB) model for lateral spreading prediction, trained on data from the 2011 Christchurch Earthquake. SHAP analysis reveals the factors driving the model's predictions, enhancing transparency and allowing for comparison with established engineering knowledge. The results demonstrate that the XGB model successfully identifies the importance of soil characteristics derived from Cone Penetration Test (CPT) data in predicting lateral spreading, validating its alignment with domain understanding. This work highlights the value of explainable machine learning for reliable and informed decision-making in geotechnical engineering and hazard assessment.

physics.geo-ph↗

arXiv2023

Differentiable programming for inverse estimation of soil permeability and design of duct banks

Underground duct banks carrying power cables dissipate heat to the surrounding soil. The amount of heat dissipated determines the current rating of cables, which in turn affects the sizing of the cables. The dissipation of heat through the surrounding soils happens through conduction and convection. The mode of heat transfer depends on the soil's thermal and hydraulic properties like diffusivity and permeability. The soil surrounding the cables could be designed to have maximum heat dissipation to have an improved current rating of cables. Differentiable programming is a novel technique that combines automatic differentiation with gradient-based optimization to minimize a loss function. Hence, differentiable programming can be used to evaluate input parameters based on output results. Given a desired heat distribution in the soil and a temperature source, we use differentiable programming to solve the inverse problem of estimating the soil permeability. In the present study, we employ differentiable programming to optimize the design of the buried duck bank and the backfill soil to improve heat dissipation. The design involves optimizing the permeability and size of the fill material compared to the surrounding natural soil. To implement automatic differentiation, we develop an inverse finite difference code in the Julia programming language and ForwardDiff package. We demonstrate the design capabilities of the differentiable programming technique to obtain the optimum permeability of the backfill material from the norm of the temperature distribution in the surrounding soil.

physics.geo-ph↗

arXiv2023

Graph Neural Network-based surrogate model for granular flows

Accurate simulation of granular flow dynamics is crucial for assessing various geotechnical risks, including landslides and debris flows. Granular flows involve a dynamic rearrangement of particles exhibiting complex transitions from solid-like to fluid-like responses. Traditional continuum and discrete numerical methods are limited by their computational cost in simulating large-scale systems. Statistical or machine learning-based models offer an alternative. Still, they are largely empirical, based on a limited set of parameters. Due to their permutation-dependent learning, traditional machine learning-based models require huge training data to generalize. To resolve these problems, we use a graph neural network, a state-of-the-art machine learning architecture that learns local interactions. Graphs represent the state of dynamically changing granular flows and the interaction laws, such as energy and momentum exchange between grains. We develop a graph neural network-based simulator (GNS) that takes the current state of granular flow and predicts the next state using Euler explicit integration by learning the local interaction laws. We train GNS on different granular trajectories. We then assess the performance of GNS by predicting granular column collapse. GNS accurately predicts flow dynamics for column collapses with different aspect ratios unseen during training. GNS is hundreds of times faster than high-fidelity numerical simulators. The model also generalizes to domains much larger than the training data, handling more than twice the number of particles than it was trained on.

physics.geo-ph↗

arXiv2023

Three-dimensional granular flow simulation using graph neural network-based learned simulator

Reliable evaluations of geotechnical hazards like landslides and debris flow require accurate simulation of granular flow dynamics. Traditional numerical methods can simulate the complex behaviors of such flows that involve solid-like to fluid-like transitions, but they are computationally intractable when simulating large-scale systems. Surrogate models based on statistical or machine learning methods are a viable alternative, but they are typically empirical and rely on a confined set of parameters in evaluating associated risks. Due to their permutation-dependent learning, conventional machine learning models require an unreasonably large amount of training data for building generalizable surrogate models. We employ a graph neural network (GNN), a novel deep learning technique, to develop a GNN-based simulator (GNS) for granular flows to address these issues. Graphs represent the state of granular flows and interactions, like the exchange of energy and momentum between grains, and GNN learns the local interaction law. GNS takes the current state of the granular flow and estimates the next state using Euler explicit integration. We train GNS on a limited set of granular flow trajectories and evaluate its performance in a three-dimensional granular column collapse domain. GNS successfully reproduces the overall behaviors of column collapses with various aspect ratios that were not encountered during training. The computation speed of GNS outperforms high-fidelity numerical simulators by 300 times.

physics.geo-ph↗

arXiv2023

An inverse analysis of fluid flow through granular media using differentiable lattice Boltzmann method

Inverse modeling of fluid flow through porous soils and reservoir rocks enables accurate determination of permeability and seepage properties critical for applications such as contaminant filtration, stability assessments, and optimization of hydrocarbon recovery. However, the solution to the inverse problem is ill-posed and sensitive to noise in measurements. Direct simulation of flow through granular media only provides forward predictions rather than inverse characterization. We present an effective method for solving inverse analysis of fluid flow through granular media. The key objectives are accurately determining boundary conditions and characterizing the physical properties of the granular media (e.g., permeability) and fluid viscosity based on the flow state. We develop a fully differentiable lattice Boltzmann Method (LBM) using Automatic Differentiation (AD) to optimize the gradients of the input features with respect to the observations. We implement a GPU-capable AD-LBM using the Domain-Specific Taichi programming language by employing lightweight tape gradients for end-to-end backpropagation. For complex flow paths in porous media, our AD-LBM approach accurately estimates the boundary conditions leading to observed steady-state velocity fields and consequently derives macro-scale permeability and fluid viscosity. Our method demonstrates significant advantages in prediction accuracy and computational efficiency, offering a powerful tool for solving inverse fluid flow problems in various applications.

physics.flu-dyn↗

arXiv2023

Accelerating Particle and Fluid Simulations with Differentiable Graph Networks for Solving Forward and Inverse Problems

We leverage physics-embedded differentiable graph network simulators (GNS) to accelerate particulate and fluid simulations to solve forward and inverse problems. GNS represents the domain as a graph with particles as nodes and learned interactions as edges. Compared to modeling global dynamics, GNS enables learning local interaction laws through edge messages, improving its generalization to new environments. GNS achieves over 165x speedup for granular flow prediction compared to parallel CPU numerical simulations. We propose a novel hybrid GNS/Material Point Method (MPM) to accelerate forward simulations by minimizing error on a pure surrogate model by interleaving MPM in GNS rollouts to satisfy conservation laws and minimize errors achieving 24x speedup compared to pure numerical simulations. The differentiable GNS enables solving inverse problems through automatic differentiation, identifying material parameters that result in target runout distances. We demonstrate the ability of GNS to solve inverse problems by iteratively updating the friction angle (a material property) by computing the gradient of a loss function based on the final and target runouts, thereby identifying the friction angle that best matches the observed runout. The physics-embedded and differentiable simulators open an exciting new paradigm for AI-accelerated design, control, and optimization.

physics.geo-ph↗

arXiv2023

3D Object Positioning Using Differentiable Multimodal Learning

This article describes a multi-modal method using simulated Lidar data via ray tracing and image pixel loss with differentiable rendering to optimize an object's position with respect to an observer or some referential objects in a computer graphics scene. Object position optimization is completed using gradient descent with the loss function being influenced by both modalities. Typical object placement optimization is done using image pixel loss with differentiable rendering only, this work shows the use of a second modality (Lidar) leads to faster convergence. This method of fusing sensor input presents a potential usefulness for autonomous vehicles, as these methods can be used to establish the locations of multiple actors in a scene. This article also presents a method for the simulation of multiple types of data to be used in the training of autonomous vehicles.

eess.SY↗

arXiv2023

Motion of a parametrically driven damped coplanar double pendulum

We present the results of linear stability of a damped coplanar double pendulum and its non-linear motion, when the point of suspension is vibrated sinusoidally in the vertical direction with amplitude $a$ and frequency $ω$. A double pendulum has two pairs of Floquet multipliers, which have been calculated for various driving parameters. We have considered the stability of a double pendulum when it is in any of its possible stationary states: (i) both pendulums are either vertically downward or upward and (ii) one pendulum is downward, and the other is upward. The damping is considered to be velocity-dependent, and the driving frequency is taken in a wide range. A double pendulum excited from its stable state shows both periodic and chaotic motion. The periodic motion about its pivot may be either oscillatory or rotational. The periodic swings of a driven double pendulum may be either harmonic or subharmonic for lower values of $a$. The limit cycles corresponding to the normal mode oscillations of a double pendulum of two equal masses are squeezed into a line in its configuration space. For unequal masses, the pendulum shows multi-period swings for smaller values of $a$ and damping, while chaotic swings or rotational motion at relatively higher values of $a$. The parametric driving may lead to stabilization of a partially or fully inverted double pendulum.

physics.class-ph↗