An Interpretable Artificial Intelligence Systems for Efficient Modeling of Functional Surrogates for High-Fidelity Computer Models

2025-03-26

AI Summary

High-fidelity computational models incur prohibitive simulation costs and hinder deployment of interpretable surrogate models. To address this, we propose DeepSurrogate: an interpretable deep surrogate model designed for functional outputs. Our method introduces a novel dual-branch deep architecture that separately captures input–output nonlinearities and spatial dependency structures, while quantifying predictive uncertainty via Monte Carlo Dropout. It disentangles spatial-indexed responses into position-invariant nonlinear effects and position-dependent spatial fields, thereby balancing physical interpretability with high-fidelity approximation. Trained on 50,000 spatial points and only 20 simulations, training completes in under 10 minutes. Evaluated on synthetic benchmarks and hurricane storm-surge simulations, DeepSurrogate achieves state-of-the-art accuracy, accelerates inference by 2–3 orders of magnitude, and supports uncertainty-aware prediction and local effect attribution. The implementation is publicly available.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Reasoning under Uncertainty: Relational Probabilistic Models
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

Surrogates for computationally expensive computer models have become increasingly important in addressing complex scientific and engineering problems. This article introduces an artificial intelligence based surrogate model, DeepSurrogate, designed for analyzing functional outputs with vector-valued inputs. The input output relationship is expressed through a sequence of spatially indexed functions, each modeling the response at a specific spatial location. These functions are decomposed into two components: one modeling nonlinear input effects, and the other capturing spatial dependence across the output domain, both implemented using deep neural networks. This architecture allows simultaneous modeling of spatial correlation in the output and complex input output mappings. A key feature of DeepSurrogate is its ability to quantify predictive uncertainty via a Monte Carlo dropout strategy, improving interpretability of the deep model. The approach is computationally efficient, handling large datasets with around 50,000 spatial locations and 20 simulation runs, with full model training and evaluation completed in under ten minutes on standard hardware. The method is validated on synthetic examples and a large scale application involving hurricane surge simulation, and is accompanied by an open-source Python implementation.

Problem

• Develops AI surrogate model for high-fidelity computer simulations
• Handles functional outputs with vector-valued inputs efficiently
• Quantifies predictive uncertainty in deep learning models

Innovation

• Deep neural networks model functional outputs
• Monte Carlo dropout quantifies predictive uncertainty
• Efficient training on large datasets