Recent advances in machine learning and sensing technologies have enabled the development of data-driven structural monitoring methods. Differentiable physics simulators offer a promising approach for solving inverse problems, such as structural damage detection. This paper presents a Differentiable Material Point Method (DiffMPM) based methodology for locating and characterizing structural damage using dynamic strain measurements. In contrast to black-box deep learning methods, the proposed method produces a physics-based, interpretable model that strictly adheres to continuum mechanics. Specifically, the structure’s MPM model is constructed in Taichi, which supports differentiable programming. Then, the MPM model’s output dynamic strain is compared against the dynamic strain generated by a model with a damaged elastic field to produce a loss. Differentiable programming allows the calculation of the gradient with respect to MPM model parameters, which can be used to update the model through gradient-based optimization algorithms such as L-BFGS-B to inversely estimate the damaged elastic field. Several damage detection strategies are also explored to enhance damage characterization, and different types of damage are modeled to assess the framework’s effectiveness under varied conditions, including noisy data. Results demonstrate that DiffMPM can accurately locate damage and has potential for detailed damage characterization, even for limited sensor placement.

This work presents a computationally efficient and robust numerical framework for simulating the dynamic behavior of Cosserat rods with contact interactions. The proposed method employs a discontinuous Galerkin (DG) formulation with a matrix-free implementation, enabling high-fidelity dynamic simulations of one-dimensional slender structures. An explicit time integration scheme governed by a stability condition ensures numerical stability, while a penalty-based {discontinuous rod-to-rod surrogate} contact model provides flexible and accurate handling of interactions with complex boundaries and surfaces. The framework is verified through multiple benchmark cases, including static bending, helical bifurcation, and multi-object contact, demonstrating its capability to capture large deformations, bifurcations, and contact dynamics inherent in rod-fabricated structures; the claimed fidelity and robustness are substantiated quantitatively by demonstrated optimal convergence rates at polynomial degrees one through three with quantified Lax--Friedrichs dissipation, an exact characteristic analysis with a rigorous CFL bound, capstan-verified frictional contact with a momentum-audited rod-to-rod surrogate, and strong MPI scaling. Owing to its scalability, stability, and versatility, the proposed method enables efficient simulation of yarn, rope, and soft robots.

Explainable Boosting Machines (EBMs) provide transparent predictions through additive shape functions, enabling direct inspection of feature contributions. However, EBMs can learn non-physical relationships that reduce their reliability in natural hazard applications. This study presents a domain-informed framework to improve the physical consistency of EBMs for lateral spreading prediction. Our approach modifies learned shape functions based on domain knowledge. These modifications correct non-physical behavior while maintaining data-driven patterns. We apply the method to the 2011 Christchurch earthquake dataset and correct non-physical trends observed in the original EBM. The resulting model produces more physically consistent global and local explanations, with an acceptable tradeoff in accuracy (4–5%).

The integration of machine learning (ML) techniques into computational fluid dynamics and heat transfer analysis represents a paradigm shift in engineering modeling. This paper presents a comprehensive review and analysis of ML-based approaches for modeling fluid flow and heat transfer phenomena in various engineering systems. Traditional computational methods, while accurate, often require substantial computational resources and time. Machine learning algorithms, including neural networks, support vector machines, and ensemble methods, offer promising alternatives for real-time prediction, optimization, and control of thermal-fluid systems. This study examines the application of supervised and unsupervised learning techniques across different engineering domains, including heat exchangers, electronic cooling systems, and renewable energy applications. We analyze the performance metrics of various ML models, discuss implementation challenges, and provide insights into future research directions. Results demonstrate that ML-based models can achieve prediction accuracies exceeding 95% while reducing computational time by orders of magnitude compared to traditional CFD simulations.

To date, analyzing data from sedimentation velocity analytical ultracentrifugation (SV-AUC) experiments has exclusively been performed using finite element method or other numerical solver-based techniques. These methods are slow, requiring repeated solving of the Lamm equation in order to obtain an accurate solution. In this paper, we demonstrate how the Lamm equation is alternatively solved accurately using machine learning’s automatic differentiation by implementing it into the loss function of an inverse physics informed neural network (PINN). Subsequently, we confirm that by implementing the Lamm equation into a physics informed deep operator network (PI-DeepONet), synthetic SV-AUC data can be easily generated and then inverted back into size distributions using a multi-layer perceptron (MLP). This combined PI-DeepONet and MLP creates an end-to-end framework, named SedNet, in which the Lamm equation is enforced via a physics-informed forward operator. We demonstrate how SedNet readily analyzes SV-AUC data and is generalized to real SV-AUC experimental data showing its potential applications as an analytical tool.

Engineering courses taught in traditional lecture-based format are often perceived as difficult by students as they struggle to understand the concepts and perform well on the assessments. Attempts made to address these issues by using innovative active-learning methods have shown promising outcomes, yet limited institutional resources and the lack of familiarity with alternative pedagogies impose limitations on the scalability and acceptance of these innovations. To overcome these challenges, this study investigates the potential of partial incorporation of problem-based learning (PBL) methods using case-studies of real-world engineering failures in a large geotechnical engineering course. It adopted a quasi-experimental and repeated measure design to compare both learning and attitudinal outcomes between students in two different sections of the course – one section utilized the traditional lecture-based methods (the comparison group), and the other section utilized case-studies as the primary pedagogical approach (referred to as the “Murder Mystery” approach). Quantitative analysis demonstrated the comparative advantage of using the Murder Mystery approach over the traditional lecture-based teaching methods on both cognitive and affective student learning outcomes. Results show that, as compared to students in the comparison section, students taught using the Murder Mystery approach performed significantly better on the final exams. Additionally, they perceived the course to be relatively less difficult by the end of the semester, retained interest in the subject over the course of the semester, and also increased their confidence. Introducing elements of active-learning methods, like PBL and case-studies, in otherwise instructor-centered classes is thus recommended to improve students’ overall engineering learning experience and the conceptual understanding.

Machine learning models for geotechnical hazard prediction can achieve high accuracy while learning physically inconsistent relationships from sparse or biased training data. Current remedies (post-hoc explainability, such as SHAP and LIME, and training-time constraints) either diagnose individual predictions approximately or restrict model capacity without providing exhaustive guarantees. This paper encodes trained tree ensembles as logical formulas in a Satisfiability Modulo Theories (SMT) solver and checks physical specifications across the entire input domain, not just sampled points. Four geotechnical specifications (water table depth, PGA monotonicity, distance safety, and flat-ground safety) are formalized as decidable logical formulas and verified via SMT against both XGBoost ensembles and Explainable Boosting Machines (EBMs) trained on the 2011 Christchurch earthquake lateral spreading dataset (7,291 sites, four features). The SMT solver either produces a concrete counterexample where a specification fails or proves that no violation exists. The unconstrained EBM (80.1

World models for embodied AI must be physically viable: constructed to answer intervention queries by representing the physical structure governing action outcomes, rather than merely predicting future observations. Existing observation-predictive world models can produce visually plausible but physically wrong rollouts. This failure is structural; distinct physical systems can look identical yet diverge under intervention. We expose this problem with controlled benchmarks that fix the visible scene while varying latent physics. We show that such models may recommend infeasible actions, mispredict interaction outcomes, or certify unsafe behavior. We argue that embodied AI requires world models that identify the simplest physical abstraction sufficient to answer an intervention query. Such a model comprises modular components, including environment representation, latent state and parameter estimation, action specification, interventional dynamics, and query-level response. An autonomous orchestrator should identify the relevant abstraction and compose compatible learned and structured components per query. When closed-form physics is unavailable, uncertain, or costly, the transition model may be analytic, simulated, learned, or hybrid, but it must preserve the structure that determines interventional outcomes. This decomposition makes the model interpretable, its components verifiable, and its outputs auditable against the query. It also provides a design principle for new world models and a feasibility test for existing ones: the right abstraction is not the most detailed model of the world, but the simplest model that preserves the distinctions relevant to the query. We demonstrate this approach on queries that existing systems fail to answer correctly, and outline how an orchestrator can dynamically assemble and adapt physically viable models for planning, control, and verification.

Neural operator methods have emerged as powerful tools for learning mappings between infinite-dimensional function spaces, yet their potential in optimal control remains largely unexplored. We focus on multi-task control problems, whose solution is a mapping from task description (e.g., cost or dynamics functions) to optimal control law (e.g., feedback policy). We approximate these solution operators using a permutation-invariant neural operator architecture. Across a range of parametric optimal control environments and a locomotion benchmark, a single operator trained via behavioral cloning accurately approximates the solution operator and generalizes to unseen tasks, out-of-distribution settings, and varying amounts of task observations. We further show that the branch-trunk structure of our neural operator architecture enables efficient and flexible adaptation to new tasks. We develop structured adaptation strategies ranging from lightweight updates to full-network fine-tuning, achieving strong performance across different data and compute settings. Finally, we introduce meta-trained operator variants that optimize the initialization for few-shot adaptation. These methods enable rapid task adaptation with limited data and consistently outperform a popular meta-learning baseline. Together, our results demonstrate that neural operators provide a unified and efficient framework for multi-task control and adaptation.

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.

Inverse problems challenge existing neural operator architectures because ill-posed inverse maps violate continuity, uniqueness, and stability assumptions. We introduce B2B^-1, an inverse basis-to-basis neural operator framework that addresses this limitation. Our key innovation is to decouple function representation from the inverse map. We learn neural basis functions for the input and output spaces, then train inverse models that operate on the resulting coefficient space. This structure allows us to learn deterministic, invertible, and probabilistic models within a single framework, and to choose models based on the degree of ill-posedness. We evaluate our approach on six inverse PDE benchmarks, including two novel datasets, and compare against existing invertible neural operator baselines. We learn probabilistic models that capture uncertainty and input variability, and remain robust to measurement noise due to implicit denoising in the coefficient calculation. Our results show consistent re-simulation performance across varying levels of ill-posedness. By separating representation from inversion, our framework enables scalable surrogate models for inverse problems that generalize across instances, domains, and degrees of ill-posedness.

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 (I-c) and normalized cone resistance (q(c1Ncs)) into 10 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- and 3-m 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.

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.

The effective stress parameter, chi, is essential for calculating the effective stress in unsaturated soils. Experimental measurements have captured different relationships between chi and the degree of saturation, S-r; however, they have not been able to explain the specific shapes of the chi-S-r curves. Theoretical solutions express S(r )as a function of a(wn) and the air-water interfacial area, a(wn) ; however, chi is difficult to predict, limiting further investigation of chi variation. This study presents an alternative micromechanical approach for studying chi 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 chi based on the suction and surface tension forces applied to each grain. Using this algorithm, we simulate the chi-S-r curve over a full hydraulic cycle for a synthetic 3D granular soil column with immobile spherical grains. We find that chi= 1 at S-r= 1 and chi= 0 at S-r= 0,while chi > S, while chi > S-r for all other saturations. The maximum divergence of chi from S-r occurs at the transition from/to the pendular regime. We also observe that the chi-S-r curve is hysteretic; chi is larger during wetting (imbibition) compared to drying (drainage) due to the larger contribution of surface tension forces.

There is increasing interest in solving partial differential equations (PDEs) by casting them as machine learning problems. Recently, there has been a spike in exploring Kolmogorov-Arnold Networks (KANs) as an alternative to traditional neural networks represented by Multi-Layer Perceptrons (MLPs). While showing promise, their performance advantages in physics-based problems remain largely unexplored. Several critical questions persist: Can KANs capture complex physical dynamics and under what conditions might they outperform traditional architectures? In this work, we present a comparative study of KANs and MLPs for learning physical systems governed by PDEs. We assess their performance when applied in deep operator networks (DeepONet) and graph network-based simulators (GNS), and test them on physical problems that vary significantly in scale and complexity. Drawing inspiration from the Kolmogorov Representation Theorem, we examine the behavior of KANs and MLPs across shallow and deep network architectures. Our results reveal that although KANs do not consistently outperform MLPs when configured as deep neural networks, they demonstrate superior expressiveness in shallow network settings, significantly outpacing MLPs in accuracy over our test cases. This suggests that KANs are a promising choice, offering a balance of efficiency and accuracy in applications involving physical systems.

Micro-scale mechanisms, such as inter-particle and particle-fluid interactions, govern the behaviour of granular systems. While particle-scale simulations provide detailed insights into these interactions, their computational cost is often prohibitive. At a recent Lorentz Center Workshop on “ Machine Learning for Discrete Granular Media ”, researchers explored how machine learning approaches can aid the development of constitutive laws and efficient data-driven surrogates for granular materials while also addressing uncertainty quantification. Attended by researchers from both the granular materials (GM) and machine learning (ML) communities, the workshop brought the ML community up to date with GM challenges. This position paper emerged from the workshop discussions. In this position paper, we define granular materials and identify seven key challenges that characterise their distinctive behaviour across various scales and regimes–ranging from gas-like to fluid-like and solid-like. Addressing these challenges is essential for developing robust and efficient models for the digital twinning of granular systems in various industrial applications. To showcase the potential of ML to the GM community, we present classical and emerging machine/deep learning techniques that have been, or could be, applied to granular materials. We reviewed sequence-based learning models for path-dependent constitutive behaviour, followed by encoder-decoder type models for representing high-dimensional data in reduced spaces. We then explore graph neural networks and recent advances in neural operator learning. The latter captures the emerging field evolution of interacting particles via efficient latent space representation. Lastly, we discuss model-order reduction and probabilistic learning techniques for high-dimensional parameterised systems, both of which are crucial for quantifying and incorporating uncertainties arising from physics-based and data-driven models. We present a typical workflow aimed at unifying data structures and modelling pipelines and guiding readers through the selection, training, and deployment of ML surrogates for granular material simulations. Finally, we illustrate the workflow’s practical use with two representative examples, focusing on granular materials in solid-like and fluid-like regimes.

We introduce a differentiable framework for zero-shot adaptive control over parametric families of nonlinear dynamical systems. Our approach integrates a function encoder-based neural ODE (FE-NODE) for modeling system dynamics with a differentiable predictive control (DPC) for offline self-supervised learning of explicit control policies. The FE-NODE captures nonlinear behaviors in state transitions and enables zero-shot adaptation to new systems without retraining, while the DPC efficiently learns control policies across system parameterizations, thus eliminating costly online optimization common in classical model predictive control. We demonstrate the efficiency, accuracy, and online adaptability of the proposed method across a range of nonlinear systems with varying parametric scenarios, highlighting its potential as a general-purpose tool for fast zero-shot adaptive control.

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.

This study introduces a novel optimization framework based on the differentiable material point method (DiffMPM) for the identification of structural and loading parameters from dynamic structural monitoring data. Structural health monitoring (SHM) methodologies are often challenged by the need to interpret limited and noisy measurements for unknown parameter identification, particularly in dynamic environments where external forces are not directly observable. DiffMPM addresses this challenge by integrating a particle-based continuum model with automatic differentiation, enabling the inference of spatially varying elastic properties and loading parameters from dynamic strain data. In contrast to conventional model updating techniques, DiffMPM provides a fully differentiable simulation pipeline that enables efficient gradient-based parameter estimation. A comprehensive series of numerical experiments validates the framework's robust performance under conditions of varying mesh resolution, measurement point density, initial parameter assumptions, and measurement sensor noise. This work highlights the potential of differentiable physics for SHM applications requiring interpretable estimation of structural and loading parameters.

We introduce a novel framework that integrates Neural Radiance Fields (NeRF) with Material Point Method (MPM) simulation to infer granular material properties from visual observations. Our approach begins by generating synthetic experimental data, simulating an plow interacting with sand. The experiment is rendered into realistic images as the photographic observations. These observations include multi-view images of the experiment's initial state and time-sequenced images from two fixed cameras. Using NeRF, we reconstruct the 3D geometry from the initial multi-view images, leveraging its capability to synthesize novel viewpoints and capture intricate surface details. The reconstructed geometry is then used to initialize material point positions for the MPM simulation, where the friction angle remains unknown. We render images of the simulation under the same camera setup and compare them to the observed images. By employing Bayesian optimization, we minimize the image loss to estimate the best-fitting friction angle. Our results demonstrate that friction angle can be estimated with an error within 2 degrees, highlighting the effectiveness of inverse analysis through purely visual observations. This approach offers a promising solution for characterizing granular materials in real-world scenarios where direct measurement is impractical or impossible.