arXiv subjects

Krishna Kumar

Publications and source records attributed to Krishna Kumar.

At least 19 recordsLinked to original sources

arXiv2026

End-to-End Learning of Safe Optimal Feedback Control in High Dimensions with Control Barrier Function Layers

We consider the problem of learning high-dimensional semi-global feedback controllers under hard safety constraints enforced by control barrier functions (CBFs). Incorporating CBFs into end-to-end policy training requires embedding a quadratic-program-based safety filter as an optimization layer, but computational and differentiation bottlenecks have largely restricted prior approaches to low-dimensional systems, typically with at most 16 state dimensions. We address this limitation by combining operator splitting with the recently developed Jacobian-Free Backpropagation (JFB) method to enable scalable end-to-end training while preserving hard safety guarantees through the CBF safety filter. We justify this training methodology theoretically using nonsmooth analysis techniques and demonstrate its effectiveness on high-dimensional multi-agent nonlinear control problems with state and control dimensions up to 1200 and 400, respectively.

cs.LG↗

arXiv2026

Path Planning in Physically Viable World Models

Robots deployed in unstructured outdoor environments often plan from scene reconstructions collected before deployment because operators cannot remap large or remote sites before every mission. As a result, robots must make long-horizon planning decisions using stale maps that assume the terrain remains unchanged, even though physical changes to the environment may render previously feasible routes unsafe or unreachable at execution time. We present a physically viable world model for evaluating what-if queries for robot navigation under future terrain change. The system augments reconstructed 3D Gaussian splat scenes with physics-based simulation to generate physically modified versions of the same environment without recollecting sensor data or rebuilding the map. We then implement a terrain-aware planner that accounts for physical events, obstacles, and deformations that are simulated by the world model. This allows robots and human operators to evaluate whether planned routes remain feasible before committing to a planned route, particularly in constrained environments where retreat or recovery may become impossible once conditions change. We evaluate the system on a real outdoor field site in Central Texas using simulated flooding across multiple severity levels. We measure route and mission feasibility as terrain conditions deteriorate under physically simulated interventions. Our results show that physically viable world models expose long-horizon route failures and rerouting behavior that are not apparent when planning only on the original reconstructed environment, allowing robots to evaluate how future terrain changes may affect route feasibility before deployment.

cs.RO↗

arXiv2026

Physically Viable World Models: A Case for Query-Conditioned Embodied AI

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.

cs.AI↗

arXiv2026

Non-Floquet oscillations of a parametrically driven rigid planar pendulum

The linear and nonlinear motions of a damped rigid planar pendulum, driven by vibrating its pivot sinusoidally, are reexamined. The pendulum is known to exhibit periodic, quasiperiodic, and chaotic motions. Floquet analysis identifies regions of instability and stability within the driving parameter space. A new type of nonlinear oscillation may occur at driving parameters where Floquet analysis predicts a stable stationary state. Such non-Floquet oscillations always have periods longer than twice the period of the vibrating pivot. The possible periods of these oscillations may be four, six, eight, or twelve times the driving period. The power spectrum of the pendulum's angular velocity during these oscillations reveals a novel feature: the two dominant response frequencies sum to the driving frequency.

physics.class-ph↗

arXiv2026

Neural Operators for Multi-Task Control and Adaptation

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.

cs.LG↗

arXiv2026

De Jure: Iterative LLM Self-Refinement for Structured Extraction of Regulatory Rules

Regulatory documents encode legally binding obligations that LLM-based systems must respect. Yet converting dense, hierarchically structured legal text into machine-readable rules remains a costly, expert-intensive process. We present De Jure, a fully automated, domain-agnostic pipeline for extracting structured regulatory rules from raw documents, requiring no human annotation, domain-specific prompting, or annotated gold data. De Jure operates through four sequential stages: normalization of source documents into structured Markdown; LLM-driven semantic decomposition into structured rule units; multi-criteria LLM-as-a-judge evaluation across 19 dimensions spanning metadata, definitions, and rule semantics; and iterative repair of low-scoring extractions within a bounded regeneration budget, where upstream components are repaired before rule units are evaluated. We evaluate De Jure across four models on three regulatory corpora spanning finance, healthcare, and AI governance. On the finance domain, De Jure yields consistent and monotonic improvement in extraction quality, reaching peak performance within three judge-guided iterations. De Jure generalizes effectively to healthcare and AI governance, maintaining high performance across both open- and closed-source models. In a downstream compliance question-answering evaluation via RAG, responses grounded in De Jure extracted rules are preferred over prior work in 73.8% of cases at single-rule retrieval depth, rising to 84.0% under broader retrieval, confirming that extraction fidelity translates directly into downstream utility. These results demonstrate that explicit, interpretable evaluation criteria can substitute for human annotation in complex regulatory domains, offering a scalable and auditable path toward regulation-grounded LLM alignment.

cs.AI↗

arXiv2026

Formal verification of tree-based machine learning models for lateral spreading

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% accuracy) violates all four specifications. A fully constrained EBM (67.2%) satisfies three of four specifications, demonstrating that iterative constraint application guided by verification can progressively improve physical consistency. A Pareto analysis of 33 model variants reveals a persistent trade-off, as none of the variants studied achieve both greater than 80% accuracy and full compliance with the specified set. SHAP analysis of specification counterexamples shows that the offending feature can rank last, demonstrating that post-hoc explanations do not substitute for formal verification. These results establish a verify-fix-verify engineering loop and a formal certification for deploying physically consistent ML models in safety-critical geotechnical applications.

cs.LG↗

arXiv2026

Domain-informed explainable boosting machines for trustworthy lateral spread predictions

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\%).

cs.LG↗

arXiv2025

A Critical Assessment of PINNs and Operator Learning for Geotechnical Engineering

Scientific machine learning (SciML) offers neural-network alternatives to numerical workflows in geotechnical engineering. This paper benchmarks multi-layer perceptrons (MLPs), physics-informed neural networks (PINNs), deep operator networks (DeepONet), and graph network simulators (GNS) against finite-difference and particle-based references on geotechnical benchmarks, and compares PINN inversion with automatic differentiation (AD) through a conventional solver. We evaluate each method for extrapolation, training, and inference cost, transfer across problem instances, and physics accuracy. An MLP trained on two years of Terzaghi consolidation fits the data, but at year ten predicts ~290 mm with ReLU and ~60 mm with tanh or sigmoid, against a reference of 99.3 mm. A PINN on a damped oscillator with a time domain inside [0,1] matches the closed form within that interval but fails outside, since the residual constrains the fit only where it is sampled. For the 1D wave equation, PINN training is ~96,000 times slower than finite-difference methods and less accurate. DeepONet avoids PINN retraining, yet for the beam on elastic foundation, its training cost equals ~1.8 million finite-difference solves, and inference is slower per query than the direct solver. GNS improves geometric transfer through local particle interactions, though formulations still need trajectories, large training sets, and substantial memory. In the inverse wave benchmark, AD through the finite-difference solver recovers the material profile in seconds with ~1% error. The results support a cautious role for SciML. Neural networks suit interpolation and pattern recognition inside validated domains, while inverse analysis should first try differentiable physics-based solvers when a reliable forward solver exists.

physics.geo-ph↗

arXiv2025

Learning Generalizable Neural Operators for Inverse Problems

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.

cs.LG↗

arXiv2025

Parameter-Efficient Conditioning for Material Generalization in Graph-Based Simulators

Graph network-based simulators (GNS) have demonstrated strong potential for learning particle-based physics (such as fluids, deformable solids, and granular flows) while generalizing to unseen geometries due to their inherent inductive biases. However, existing models are typically trained for a single material type and fail to generalize across distinct constitutive behaviors, limiting their applicability in real-world engineering settings. Using granular flows as a running example, we propose a parameter-efficient conditioning mechanism that makes the GNS model adaptive to material parameters. We identify that sensitivity to material properties is concentrated in the early message-passing (MP) layers, a finding we link to the local nature of constitutive models (e.g., Mohr-Coulomb) and their effects on information propagation. We empirically validate this by showing that fine-tuning only the first few (1-5) of 10 MP layers of a pretrained model achieves comparable test performance as compared to fine-tuning the entire network. Building on this insight, we propose a parameter-efficient Feature-wise Linear Modulation (FiLM) conditioning mechanism designed to specifically target these early layers. This approach produces accurate long-term rollouts on unseen, interpolated, or moderately extrapolated values (e.g., up to 2.5 degrees for friction angle and 0.25 kPa for cohesion) when trained exclusively on as few as 12 short simulation trajectories from new materials, representing a 5-fold data reduction compared to a baseline multi-task learning method. Finally, we validate the model's utility by applying it to an inverse problem, successfully identifying unknown cohesion parameters from trajectory data. This approach enables the use of GNS in inverse design and closed-loop control tasks where material properties are treated as design variables.

cs.LG↗

arXiv2025

Zero-Shot Function Encoder-Based Differentiable Predictive Control

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.

eess.SY↗

arXiv2025

Stability of Transformers under Layer Normalization

Despite their widespread use, training deep Transformers can be unstable. Layer normalization, a standard component, improves training stability, but its placement has often been ad-hoc. In this paper, we conduct a principled study on the forward (hidden states) and backward (gradient) stability of Transformers under different layer normalization placements. Our theory provides key insights into the training dynamics: whether training drives Transformers toward regular solutions or pathological behaviors. For forward stability, we derive explicit bounds on the growth of hidden states in trained Transformers. For backward stability, we analyze how layer normalization affects the backpropagation of gradients, thereby explaining the training dynamics of each layer normalization placement. Our analysis also guides the scaling of residual steps in Transformer blocks, where appropriate choices can further improve stability and performance. Our numerical results corroborate our theoretical findings. Beyond these results, our framework provides a principled way to sanity-check the stability of Transformers under new architectural modifications, offering guidance for future designs.

cs.LG↗

arXiv2025

Zero-Shot Transferable Solution Method for Parametric Optimal Control Problems

This paper presents a transferable solution method for optimal control problems with varying objectives using function encoder (FE) policies. Traditional optimization-based approaches must be re-solved whenever objectives change, resulting in prohibitive computational costs for applications requiring frequent evaluation and adaptation. The proposed method learns a reusable set of neural basis functions that spans the control policy space, enabling efficient zero-shot adaptation to new tasks through either projection from data or direct mapping from problem specifications. The key idea is an offline-online decomposition: basis functions are learned once during offline imitation learning, while online adaptation requires only lightweight coefficient estimation. Numerical experiments across diverse dynamics, dimensions, and cost structures show our method delivers near-optimal performance with minimal overhead when generalizing across tasks, enabling semi-global feedback policies suitable for real-time deployment.

math.OC↗

arXiv2025

From images to properties: a NeRF-driven framework for granular material parameter inversion

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.

cs.CV↗

arXiv2025

SetONet: A Set-Based Operator Network for Solving PDEs with Variable-Input Sampling

Most neural-operator surrogates for PDEs inherit from DeepONet-style formulations the requirement that the input function be sampled at a fixed, ordered set of sensors. This assumption limits applicability to problems with variable sensor layouts, missing data, point sources, and sample-based representations of densities. We propose SetONet, which addresses this gap by recasting the operator input as an unordered set of coordinate-value observations and encoding it with permutation-invariant aggregation inside a standard branch-trunk operator network while preserving the DeepONet synthesis mechanism and lightweight end-to-end training. A structured variant, SetONet-Key, aggregates sensor information through learnable query tokens and a position-only key pathway, thereby decoupling sampling geometry from sensor values. The method is assessed on four classical operator-learning benchmarks under fixed layouts, variable layouts, and evaluation-time sensor drop-off, and on four problems with inherently unstructured point-cloud inputs, including heat conduction with multiple point sources, advection-diffusion, phase-screen diffraction, and optimal transport problems. In parameter-matched studies, SetONet-Key achieves lower error than the DeepONet baseline on fixed-sensor benchmarks and remains reliable when layouts vary or sensors are dropped at evaluation. Comparisons across pooling rules show that attention-based aggregation is typically more robust than mean or sum pooling. On the point-cloud problems, SetONet operates directly on the native input representation, without rasterization or multi-stage preprocessing, and outperforms the larger VIDON baseline.

cs.LG↗

arXiv2025

MLPs and KANs for data-driven learning in physical problems: A performance comparison

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.

cs.LG↗

arXiv2025

Towards scientific machine learning for granular material simulations -- challenges and opportunities

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. Attended by researchers from both the granular materials (GM) and machine learning (ML) communities, a recent Lorentz Center Workshop on "Machine Learning for Discrete Granular Media" brought the ML community up to date with GM challenges. This position paper emerged from the workshop discussions. 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 digital twins for 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. We then explore graph neural networks and recent advances in neural operator learning. Lastly, we discuss model-order reduction and probabilistic learning techniques for high-dimensional parameterised systems, which are crucial for quantifying uncertainties arising from physics-based and data-driven models. We present a 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.

cond-mat.soft↗