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.

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\%).

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.

Deep Learning in Geotechnical Engineering: A Critical Assessment of PINNs and Operator Learning

Deep learning methods -- physics-informed neural networks (PINNs), deep operator networks (DeepONet), and graph network simulators (GNS) -- are increasingly proposed for geotechnical problems. This paper tests these methods against traditional solvers on canonical problems: wave propagation and beam-foundation interaction. PINNs run 90,000 times slower than finite difference with larger errors. DeepONet requires thousands of training simulations and breaks even only after millions of evaluations. Multi-layer perceptrons fail catastrophically when extrapolating beyond training data -- the common case in geotechnical prediction. GNS shows promise for geometry-agnostic simulation but faces scaling limits and cannot capture path-dependent soil behavior. For inverse problems, automatic differentiation through traditional solvers recovers material parameters with sub-percent accuracy in seconds. We recommend: use automatic differentiation for inverse problems; apply site-based cross-validation to account for spatial autocorrelation; reserve neural networks for problems where traditional solvers are genuinely expensive and predictions remain within the training envelope. When a method is four orders of magnitude slower with less accuracy, it is not a viable replacement for proven solvers.

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.

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.

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.

AdversariaL attacK sAfety aLIgnment(ALKALI): Safeguarding LLMs through GRACE: Geometric Representation-Aware Contrastive Enhancement- Introducing Adversarial Vulnerability Quality Index (AVQI)

Adversarial threats against LLMs are escalating faster than current defenses can adapt. We expose a critical geometric blind spot in alignment: adversarial prompts exploit latent camouflage, embedding perilously close to the safe representation manifold while encoding unsafe intent thereby evading surface level defenses like Direct Preference Optimization (DPO), which remain blind to the latent geometry. We introduce ALKALI, the first rigorously curated adversarial benchmark and the most comprehensive to date spanning 9,000 prompts across three macro categories, six subtypes, and fifteen attack families. Evaluation of 21 leading LLMs reveals alarmingly high Attack Success Rates (ASRs) across both open and closed source models, exposing an underlying vulnerability we term latent camouflage, a structural blind spot where adversarial completions mimic the latent geometry of safe ones. To mitigate this vulnerability, we introduce GRACE - Geometric Representation Aware Contrastive Enhancement, an alignment framework coupling preference learning with latent space regularization. GRACE enforces two constraints: latent separation between safe and adversarial completions, and adversarial cohesion among unsafe and jailbreak behaviors. These operate over layerwise pooled embeddings guided by a learned attention profile, reshaping internal geometry without modifying the base model, and achieve up to 39% ASR reduction. Moreover, we introduce AVQI, a geometry aware metric that quantifies latent alignment failure via cluster separation and compactness. AVQI reveals when unsafe completions mimic the geometry of safe ones, offering a principled lens into how models internally encode safety. We make the code publicly available at https://anonymous.4open.science/r/alkali-B416/README.md.

SetONet: A Deep Set-based Operator Network for Solving PDEs with permutation invariant variable input sampling

Neural operators, particularly the Deep Operator Network (DeepONet), have shown promise in learning mappings between function spaces for solving differential equations. However, standard DeepONet requires input functions to be sampled at fixed locations, limiting its applicability in scenarios with variable sensor configurations, missing data, or irregular grids. We introduce the Set Operator Network (SetONet), a novel architecture that integrates Deep Sets principles into the DeepONet framework to address this limitation. The core innovation lies in the SetONet branch network, which processes the input function as an unordered \emph{set} of location-value pairs. This design ensures permutation invariance with respect to the input points, making SetONet inherently robust to variations in the number and locations of sensors. SetONet learns richer, spatially-aware input representations by explicitly processing spatial coordinates and function values. We demonstrate SetONet's effectiveness on several benchmark problems, including derivative/anti-derivative operators, 1D Darcy flow, and 2D elasticity. Results show that SetONet successfully learns operators under variable input sampling conditions where standard DeepONet fails. Furthermore, SetONet is architecturally robust to sensor drop-off; unlike standard DeepONet, which requires methods like interpolation to function with missing data. Notably, SetONet can achieve comparable or improved accuracy over DeepONet on fixed grids, particularly for nonlinear problems, likely due to its enhanced input representation. SetONet provides a flexible and robust extension to the neural operator toolkit, significantly broadening the applicability of operator learning to problems with variable or incomplete input data.

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.