The Inference Report

We describe an adaptive market-making architecture that preserves the analytical structure of the Avellaneda--Stoikov framework while introducing a successor measure-style adaptation mechanism. In our paper we keep Avellaneda--Stoikov fast Hamilton--Jacobi--Bellman structure and make it adaptive to changing market regimes and trading objectives. The central idea is to separate market dynamics from the trading objective. The market state determines a low-dimensional set of Avellaneda--Stoikov parameters, while recent realized rewards determine a low-dimensional objective vector. The HJB forward map then converts this objective into optimal bid and ask quotes through a scalarization of future reward features.

Hypergraphs have the capacity to capture higher-dimensional relationships among entities across various domains, making them a subject of growing interest within the research community for understanding the structure and dynamics of complex systems. However, a key challenge is the derivation of hypergraph representations from time series data in situations where the structure of the hypergraph is limited or absent. In this study, we propose a model that constructs a dynamic hypergraph representation for multivariate time series without relying on prior knowledge of the data. This is achieved by applying community detection to the time series and transforming the resulting communities, obtained through an attention mechanism, into a hypergraph using a clique-based technique. Hypergraph representations are derived from different time series datasets, and the resulting hypergraphs are then used by a Dynamic Hypergraph Attention Convolution Network (DHACN) for multivariate time series predictions. This research advances the field of hypergraph representation by introducing a novel approach that is better suited to uncover high-order relationships without prior knowledge.

Construction projects frequently experience schedule delays and forecasting uncertainty due to variability in labor productivity, material availability, weather conditions, and project coordination. Conventional deterministic scheduling methods such as the Critical Path Method (CPM) assume fixed activity durations and therefore cannot adequately represent dynamic project uncertainty. This study presents a Bayesian-Monte Carlo probabilistic schedule updating framework for construction digital twin environments. The proposed methodology integrates stochastic activity-duration modeling, Bayesian recursive updating, Monte Carlo simulation, and uncertainty propagation within a unified computational framework for adaptive schedule forecasting. Activity durations are modeled using lognormal probability distributions and continuously updated through Bayesian inference as new project observations become available. Monte Carlo simulation is then used to propagate updated uncertainty throughout project networks and generate probabilistic completion-time forecasts, delay-risk estimates, and activity criticality measures. Simulation experiments using PSPLIB benchmark project networks demonstrate that the proposed framework improves forecasting accuracy and uncertainty representation compared with deterministic CPM and static probabilistic scheduling approaches. The framework further supports adaptive project forecasting through integration of BIM reports, drone observations, IoT telemetry, productivity logs, and site monitoring data.

Dimensionality reduction is essential in simulation-based shape design, where high-dimensional parameterizations hinder optimization, surrogate modeling, and systematic design-space exploration. Parametric Model Embedding (PME) addresses this issue by constructing reduced variables from geometric information while preserving an explicit backmapping to the original design parameters. However, PME is intrinsically linear and may become inefficient when the sampled design space is governed by nonlinear geometric variability. This paper introduces a nonlinear extension of PME, denoted NLPME. The proposed framework preserves the defining principle of PME -- geometry-driven latent variables and parameter-mediated reconstruction -- while replacing the linear reduced subspace with a nonlinear latent representation. Geometry is not reconstructed directly from the latent variables; instead, the latent representation is decoded into admissible design parameters, and the corresponding geometry is recovered through a forward parametric map. The method is assessed on a bio-inspired autonomous underwater glider with a 32-dimensional parametric shape description and a CAD-based geometry-generation process. NLPME reaches a 5\% reconstruction-error threshold with \(N=5\) latent variables, compared with \(N=8\) for linear PME, and a 1\% threshold with \(N=9\), compared with \(N=15\) for PME. Comparison with a deep autoencoder shows that most of the nonlinear compression gain can be retained while preserving an explicit backmapping to the original design variables. The results establish NLPME as a compact, admissible, and engineering-compatible nonlinear reduced representation for parametric shape design spaces.

Full-vehicle crash simulations are computationally expensive, limiting their use in iterative design exploration. This work investigates learned hybrid surrogate models (MeshTransolver, MeshGeoTransolver, and MeshGeoFLARE) for predicting time-resolved structural deformation fields in an industrial lateral pole-impact benchmark. We evaluate whether neural surrogates can reproduce full-field crash kinematics with sufficient accuracy, spatial regularity, and structural plausibility for engineering interpretation. The proposed architectures combine local mesh message passing, geometry-aware global attention, and sparse contact-aware correction for autoregressive crash rollout. We compare mesh-based graph neural networks, attention-based geometric models, and hybrid architectures under a common training and hyperparameter configuration. The hybrid models capture both short-range structural interactions and long-range deformation patterns, while a sparse contact-aware variant assesses the effect of dynamic proximity interactions during rollout. On a 25-sample full-vehicle test set, the best hybrid model achieves a temporal mean root-mean-square error of 3.20 mm. While geometry-aware attention baselines are quantitatively competitive, qualitative side-view inspection shows they can introduce local spatial noise and deformation irregularities that complicate structural interpretation. In contrast, hybrid mesh-attention models provide the best balance between scalar accuracy, survival-space consistency, and physically interpretable displacement fields. These results suggest that crash surrogate assessment should combine global error metrics with downstream safety-relevant quantities and qualitative field inspection. The proposed methodology enables fast full-field predictions while preserving essential structural information for industrial crash-engineering analysis.

The escalating complexity of modern machine learning necessitates solving challenging non-convex optimization problems, particularly in high-dimensional regimes and scenarios contaminated by gross outliers. Traditional approaches, relying on convex relaxations or specialized local search heuristics, frequently succumb to suboptimal local minima and fail to recover the true underlying discrete structures. In this paper, we propose treating these non-convex challenges as a global search problem and introduce a unified framework based on Quantum-Inspired Evolutionary Optimization (QIEO). By leveraging a probabilistic representation inspired by quantum superposition, QIEO maintains a global view of the search space, enabling it to tunnel through local optima that trap conventional gradient-based and greedy solvers. We comprehensively evaluate QIEO across diverse non-convex applications, including sparse signal recovery (gene expression analysis and compressed sensing) and robust linear regression. Extensive benchmarking against state-of-the-art continuous solvers (ADAM, Differential Evolution), classical metaheuristics (Genetic Algorithms), and specialized non-convex algorithms (Iterative Hard Thresholding) demonstrates that QIEO consistently achieves superior structural fidelity, lower mean squared error, and enhanced robustness without support inflation. Our findings suggest that embracing a quantum-inspired global search provides a resilient, unified paradigm for overcoming the inherent intractability of discrete nonconvex machine learning landscapes.