Unified cost-aware autonomous inference for geotechnical engineering: formalism, examples, and application to compaction field data

We propose a unified, cost-aware inference framework that casts geotechnical reasoning as symbolic planning over a directed hypergraph of “providers”, modular units representing equations, empirical correlations, numerical/ML surrogates, practitioner input, and physical tests. Each provider declares explicit input–output relations, costs, and metadata, enabling auditable inference chains and strategic data acquisition. The architecture supports bidirectional algebraic/numerical reasoning, a memory layer for context reuse, and reinforcement-guided cost tuning that arbitrates among competing providers while preserving exploration. Natural-language interfaces and a structured explanation module render stepwise justifications, cumulative costs, and provenance suitable for regulatory and peer audit. The first part of the paper develops the formalism and demonstrative examples, including parameter inference, measurement planning, and model calibration, to illustrate transparent, multimodal decision-making under resource constraints. We then validate the framework on field data from a compacted test lot, combining Lightweight Deflectometer (LWD) responses with Nuclear Density Gauge (NDG) measurements. Two external providers are integrated under uniform single-output, cost semantics: (i) a physics-guided surrogate coupling mechanistic priors with residual learning, and (ii) a spatial Gaussian-process baseline using LWD modulus and spatial information. A UCB-based mechanism updates provider costs from predictive errors and learns to favour the more accurate path. In this field study, the physics-guided route improves density-prediction fidelity relative to the field-only baseline while maintaining an end-to-end, transparent audit trail of the inference process.