⚡ electrical engineering

Physics-Informed and Surrogate-Assisted Cost Optimization of Fire Protection Materials

This study introduces a novel physics-informed hybrid optimization framework that integrates Finite Difference heat transfer simulations, a CatBoost surrogate cost model, and a Genetic Algorithm to automatically discover a cost-optimal passive fire protection material configuration that meets R180 safety standards at a significantly lower cost than traditional commercial alternatives.

Original authors: Ivan Dmitriev

Published 2026-06-29

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Ivan Dmitriev

Original paper licensed under CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are building a house of steel. If a fire starts, that steel will melt and the house could collapse in minutes. To stop this, engineers wrap the steel in a thick blanket of fire-proof material.

For decades, picking this blanket has been like shopping in a store with a very rigid, outdated catalog. You have to choose from pre-made sizes (like a 50mm blanket or a 60mm blanket), even if your steel beam only needs a 52mm blanket to be safe. This forces builders to buy "oversized" blankets that are thicker and more expensive than necessary, wasting money and materials.

This paper introduces a new way to design these blankets using Artificial Intelligence (AI) and Physics. Instead of picking from a catalog, the AI acts like a master chef who invents a perfect recipe from scratch that costs the least amount of money while still keeping the steel safe.

Here is how the system works, broken down into simple parts:

1. The Three-Part Team

The researchers built a digital team with three distinct roles to solve this puzzle:

The Physics Engine (The Safety Inspector): This is a strict rule-follower based on European safety codes (Eurocode 3). It simulates a fire (specifically the "ISO 834" fire, which is like a standard wood fire in a building) and calculates exactly how hot the steel gets. If the steel gets hotter than 500°C (the point where it starts to fail), the design is rejected.
The AI Price Predictor (The Shopper): This is a machine learning model trained on data from 533 real fire-protection products sold in Germany, Austria, and Switzerland. It learns the weird, non-linear way companies price things. For example, it knows that a 60mm board might cost much more than a 50mm board, not just because it's bigger, but because of how factories make them. It acts as a "surrogate" (a fast stand-in) for checking prices without needing to call a supplier.
The Genetic Algorithm (The Evolutionary Explorer): This is the creative part. Imagine a population of 100 imaginary blankets. Each has random traits: different thickness, different density, and different heat-blocking abilities. The AI tests them all. The "losers" (too expensive or unsafe) are discarded. The "winners" (safe and cheap) are mixed together to create a new generation. Over 100 generations, the blankets evolve into the perfect, most efficient design.

2. The "Digital Phenotype"

The result of this evolutionary process is a "Digital Phenotype." Think of this as a blueprint for a material that doesn't exist in a store yet, but could be made.

The AI discovered a "Goldilocks" solution:

Thickness: 78.2 mm (not a round number like 80mm).
Density: 56.0 kg/m³ (a specific, lightweight density).
Cost: Predicted at 23 EUR per square meter.

This specific combination keeps the steel below 500°C for 180 minutes (3 hours), meeting the strict "R180" safety rating.

3. Why This is Different

The paper highlights a few key discoveries that make this approach special:

The "Staircase" of Prices: The researchers found that material prices aren't a smooth slope; they are like a staircase. You can't buy a "half-step" price. Traditional math tools (which look for smooth slopes) fail here. The AI's "Genetic Algorithm" is like a monkey jumping up and down the stairs to find the lowest step, whereas other methods might get stuck on a high step.
The "Dry" Safety Net: The AI was programmed to be conservative. It assumes the insulation is completely dry (ignoring the fact that real materials might have a little moisture that helps cool things down). This means the AI designs a "super-safe" blanket that would still work even if the material was bone-dry and old.
No Magic Tricks: The AI didn't invent a magical, impossible material. It found a "recipe" that fits perfectly within the family of "Rock Fiber" (mineral wool) materials that already exist. It just found the exact right mix of thickness and density that manufacturers haven't optimized for yet.

4. The Result: Saving Money Without Risk

The study claims that by using this "Generative Design" approach, engineers could save 12% to 18% on material costs compared to standard catalog choices.

Instead of buying a pre-made 80mm blanket because the catalog says "use 80mm for this beam," the AI says, "Actually, a custom 78.2mm blanket with this specific density will do the exact same job for less money."

Summary

In short, this paper shows that by combining physics simulations (to ensure safety) with AI (to understand market prices), we can stop guessing and start designing fire protection. It moves us from "picking the closest option from a shelf" to "growing the perfect, cheapest solution for the specific job."

The authors have even shared their data and code so other engineers can use this "Universal Machine Learning Compiler" to design safer, cheaper buildings.

Technical Summary: Physics-Informed and Surrogate-Assisted Cost Optimization of Fire Protection Materials

1. Problem Statement

The structural integrity of steel elements under fire conditions is critical for building safety, yet traditional design methodologies for Passive Fire Protection (PFP) are often inefficient. Current practices rely on prescriptive selection from manufacturer catalogs, frequently resulting in oversized components that fail to minimize material usage or cost. These methods are constrained by:

Discrete Market Pricing: The PFP market operates on "quantized" pricing tiers rather than a smooth cost-performance continuum, making continuous optimization difficult.
Data Scarcity: High-fidelity experimental fire testing is expensive and destructive, leading to sparse datasets that hinder the training of robust machine learning models.
Forward vs. Inverse Limitations: Existing tools primarily solve "forward problems" (predicting failure times for known materials) rather than "inverse problems" (identifying the optimal material properties to meet safety constraints at minimum cost).
Lack of Economic Integration: Previous optimization frameworks often ignore real-world market economics, focusing solely on thermophysical performance or operational costs.

2. Methodology

The study proposes a novel Physics-Informed and Surrogate-Assisted Inverse Design Framework, implemented as a modular Universal Machine Learning Compiler (UMLC). The methodology integrates three core components:

A. Data Acquisition and "Digital Phenotype" Generation

Dataset: A dataset of 1,657 commercial fire protection items was compiled from 2025 DACH region (Germany, Austria, Switzerland) price lists. After filtering for structural relevance (boards, slabs, mats) and cleaning, a final operational dataset of N=533 materials was established.
Material DNA: To address data sparsity in thermal conductivity curves, the authors developed a Type-Based Polynomial Imputation strategy. Thermal conductivity $\lambda(T)$ is modeled as a second-order polynomial ( $\lambda(T) = k_2 T^2 + k_1 T + k_0$ ). For materials with incomplete data, the "shape" (curvature coefficients $k_1, k_2$ ) is transferred from the material's chemical family, while the base coefficient ( $k_0$ ) is anchored to the single available data point. This creates a continuous "Digital Phenotype" for each material.

B. Surrogate Cost Modeling

Objective: To predict market cost ( $C_{mat}$ ) based on physical descriptors without relying on static lookup tables.
Model Selection: A "Model Tournament" compared various algorithms (Linear Regression, SVM, MLP, Random Forest, XGBoost, CatBoost). CatBoost was selected as the surrogate engine due to its superior performance in handling tabular data and non-linear, quantized pricing structures (Median Squared Error $\approx$ 180, $R^2 \approx$ 0.77).
Features: The input vector includes thickness ( $d_p$ ), density ( $\rho$ ), and the three thermal conductivity coefficients ( $k_2, k_1, k_0$ ).

C. Physics-Driven Optimization Loop

Physics Solver: A numerical Finite Difference Method (FDM) solver, compliant with Eurocode 3 (EN 1993-1-2), calculates the steel temperature evolution under the standard ISO 834 fire curve. The solver enforces a hard safety constraint: steel temperature must not exceed 500°C within 180 minutes (R180).
Optimization Algorithm: A Genetic Algorithm (GA) performs a global heuristic search to minimize the composite loss function:
$\mathcal{F}(G) = \frac{1}{Cost_{pred} + \mathcal{P}_{safety} + \mathcal{P}_{risk}}$
Uncertainty Quantification: To prevent the GA from exploiting "blind spots" in the surrogate model (hallucinating physically impossible materials), a Distance-Based Uncertainty Quantification (DUQ) mechanism was implemented. Using a K-Nearest Neighbors (KNN) density estimator, solutions falling outside the empirical training manifold are penalized, ensuring the generated "Digital Phenotypes" remain physically credible.

3. Key Results

The framework successfully identified a global optimum for R180 fire resistance:

Optimal Configuration: A mineral wool board with a thickness of 78.2 mm and a density of 56.0 kg/m³.
Thermal Performance: Numerical verification confirmed the solution maintains steel temperatures below 487.7°C at the 180-minute mark, providing a 12.3°C safety margin.
Economic Performance: The predicted market cost is 23 EUR/m², significantly lower than the average cost of compliant commercial alternatives.
Cost Landscape Topology: The analysis revealed that the cost landscape is non-convex and quantized, characterized by discrete price cliffs and plateaus. This confirmed that gradient-based optimizers would fail, validating the necessity of tree-based surrogates and evolutionary search.
Sensitivity Analysis: The solution is highly sensitive to thickness (a -3.5% deviation causes failure) but surprisingly insensitive to density, allowing the optimizer to aggressively minimize density to reduce cost without compromising thermal resistance.

4. Significance and Claims

The paper positions this work as a paradigm shift from prescriptive material selection to automated, cost-driven material discovery.

Generative Design: The study demonstrates that AI can identify optimal material configurations ("Digital Phenotypes") that do not currently exist in manufacturer catalogs but are physically realizable within known material classes (specifically industrial rock fiber).
Economic Efficiency Gap: The framework reveals a "Precision Advantage," identifying that standardized catalog rounding leads to a 12–18% material reduction compared to exact physical requirements.
Hybrid Validation: By coupling machine learning with a "Hard Simulation" physics loop, the study overcomes the "Black Box" limitations of pure data-driven models, ensuring that cost-optimized solutions are thermodynamically valid and safe.
Data Contribution: The authors publish the operational dataset of 533 structural protection materials and the underlying 1,657-item raw dataset to address the "Data Starvation" bottleneck in fire engineering research.

The authors conclude that this framework provides a scalable template for inverse design in civil engineering, enabling the discovery of safety solutions where cost and structural integrity are balanced through automated, performance-driven optimization.