⚡ electrical engineering

Physics-Constrained Conditional Generative Adversarial Networks for Synthetic Seismic Ground Motion Generation in Andean Low-Seismicity Subduction Zones: A Data-Augmentation Framework with Engineering Validation for Peru

This study introduces a physics-constrained conditional GAN framework that generates engineering-compliant synthetic seismic ground motions for data-scarce Andean subduction zones, significantly reducing hazard uncertainty and enabling cost-effective retrofitting strategies for Peru's informal settlements.

Original authors: PAUL RICARDO PRUDENCIO GALVEZ

Published 2026-06-29

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CC BY 4.0

Original authors: PAUL RICARDO PRUDENCIO GALVEZ

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

The Big Problem: The "Empty Library" of Earthquakes

Imagine you are trying to learn how to bake the perfect cake, but you only have three recipes to study. Most of the world's best bakeries (like Japan or California) have thousands of recipes, so they know exactly how to make a cake that won't collapse.

But in places like the central coast of Peru, the "earthquake library" is almost empty. There are very few recorded earthquakes there because they happen rarely (sometimes only once every 150 years). Because engineers don't have enough real earthquake data, they are guessing how buildings should be built. This leads to two bad outcomes:

Under-designed: Buildings are too weak and might fall down.
Over-designed: Buildings are built with too much steel and concrete, wasting money and resources.

The Old Solution: The "Blindfolded Artist"

Engineers have tried to use computers to invent fake earthquake records to fill the library.

Old Math Methods: These need a huge library (100+ real records) to work. Since Peru doesn't have that, these methods fail.
Old AI (GANs): Newer AI models can learn from small libraries (even just 30 records). However, these AI models are like blindfolded artists. They can draw a picture that looks like an earthquake, but if you look closely, the physics are wrong. They might create an earthquake that has "negative energy" (which is impossible in real life) or shakes at frequencies that don't make sense. Engineers can't use these drawings because they don't follow the laws of physics.

The New Solution: The "Physics-Checking Chef"

This paper introduces a new AI model called a physics-constrained conditional GAN (pc-cGAN). Think of this not as a blindfolded artist, but as a chef who is strictly supervised by a food safety inspector.

The AI tries to generate fake earthquake records, but before it can "serve" the dish, it must pass three strict tests based on real engineering rules:

The "Shake-Test" (PSA): Does the fake earthquake shake buildings with the right intensity at the right speed? (Based on US and Peruvian building codes).
The "Energy-Test" (Arias Intensity): Does the fake earthquake have the right amount of total energy? It can't create energy out of thin air, nor can it disappear.
The "Soil-Test" (Vs30): Does the shaking match the type of ground it's on? Shaking on soft mud feels different than shaking on hard rock. The AI must get this right.

If the AI fails any of these tests, it has to try again. It keeps learning until it produces a fake earthquake that is 98% compliant with real-world physics.

The Results: A Better Map for Peru

The researchers trained this AI using 213 real earthquake records from Peru's public network. They then tested it on 40 records the AI had never seen.

Accuracy: The AI's fake earthquakes matched real ones with a score of 0.94 out of 1.0. (The old methods only scored around 0.70).
Reliability: 98% of the AI's outputs passed the physics tests. The old AI methods only passed 32% of the time.
The Impact: By using this AI to fill in the gaps in Peru's earthquake library, the uncertainty in safety maps dropped by 38%.

Why This Matters for Lima

In Lima, about 70% of the buildings are informal settlements (homes built without official permits or engineering checks). These are the most vulnerable.

Because this new AI can create thousands of realistic, physics-compliant earthquake scenarios from very little data, engineers can now:

Better predict how these informal homes will react to a big earthquake.
Create cheaper, more accurate retrofitting guidelines (how to strengthen existing homes).
Stop guessing and start designing with confidence, potentially saving lives and money.

The Bottom Line

This paper proves that you don't need a massive library of earthquake data to build safe structures in low-earthquake regions. By teaching AI to follow the strict rules of physics (like a chef following a recipe), we can generate high-quality, realistic earthquake data that helps engineers protect people in places like Peru, even when real data is scarce.

Technical Summary: Physics-Constrained Conditional GANs for Synthetic Seismic Ground Motion in Andean Low-Seismicity Zones

Problem Statement
Seismic hazard assessment in low-seismicity regions—defined as areas with fewer than 10 historical records of magnitude $M_w > 6.5$ earthquakes—faces a critical data scarcity challenge. While these regions harbor 60% of the global population, they account for only 12% of worldwide seismic records. This scarcity introduces hazard-map uncertainties of up to 45%, leading to infrastructure that is either underdesigned or overdesigned. Traditional stochastic simulation methods require catalogues exceeding 100 records to function effectively, a threshold unattainable in Andean subduction zones where recurrence intervals for major events exceed 150 years. Conversely, while unconstrained Generative Adversarial Networks (GANs) can learn from smaller datasets (fewer than 30 records), they frequently generate non-physical accelerograms (e.g., negative energy epochs, impossible spectral peaks) that are incompatible with engineering design standards and Performance-Based Earthquake Engineering (PBEE).

Methodology
The study proposes a Physics-Constrained Conditional Generative Adversarial Network (pc-cGAN) specifically calibrated for the Nazca-plate subduction kinematics of the central Peruvian coast.

Dataset: The model was trained on 213 public three-component accelerograms from the Peruvian National Seismic Network (RSNP), covering magnitudes $M_w$ 6.5–8.0, with metadata including epicentral distance, focal depth, and shear-wave velocity ( $V_{s30}$ ). Validation was performed on a held-out set of 40 records using 10-fold cross-validation.
Architecture:
- Generator: Accepts a 100-dimensional Gaussian latent vector concatenated with a conditioning vector $c = [M_w, R_{epi}, V_{s30}]$ . It utilizes five transposed convolutional layers with LeakyReLU activation and batch normalization to upsample the input into a 6,000-sample (60 s at 100 Hz) acceleration time history.
- Discriminator: A four-layer convolutional network with Dropout ( $p=0.3$ ) that distinguishes between real and synthetic signals conditioned on the same parameters.
Physics-Constrained Loss Function: The core innovation is a weighted multi-objective loss function ( $L_{total}$ $L_{t o t a l}$ ) that embeds three verifiable civil engineering constraints:
1. Pseudo-Spectral Acceleration (PSA) Matching: Enforces compliance with ASCE 7–22 and Norma E.030-2018 by minimizing the Mean Squared Error (MSE) between synthetic and target PSA curves at periods $T \in \{0.2, 0.5, 1.0, 2.0\}$ s.
2. Seismic Energy Conservation: Ensures the Arias Intensity ( $I_a$ ) and Cumulative Absolute Velocity (CAV) of synthetic signals align with physical laws (Hanks & Kanamori, 1979; FEMA 440).
3. Shear-Wave Velocity Compatibility: Enforces spectral compatibility based on $V_{s30}$ and soil properties (Aki & Richards, 2002).
- The total loss is formulated as $L_{total} = L_{adv} + \lambda_1 L_{PSA} + \lambda_2 L_{energy} + \lambda_3 L_{Vs}$ , with weights calibrated via grid search ( $\lambda_1=0.40, \lambda_2=0.30, \lambda_3=0.30$ ).
Validation: Synthetic records were validated against Single Degree of Freedom (SDOF) dynamic equilibrium equations and Peruvian seismic base shear formulations (Norma E.030-2018).

Key Contributions

Architecture: Development of a pc-cGAN that simultaneously operates on small catalogues characteristic of Andean subduction zones while embedding verifiable civil engineering physics directly into the loss function.
Benchmarking: A 10-fold cross-validated comparison demonstrating that the proposed model outperforms both traditional stochastic simulations and unconstrained GANs.
Site-Specific Application: Demonstration of a 38% reduction in seismic-hazard uncertainty for the central Peruvian coast (Lima–Ica), specifically addressing the risk assessment of informal settlements which constitute 70% of Lima's building stock.
Scalability: An analysis showing the framework's potential applicability to other data-scarce Latin American subduction zones (e.g., Chile, Ecuador, Colombia) with minimal retraining.

Results
The pc-cGAN achieved the following performance metrics on the test set ( $n=40$ ):

PSA Correlation: A Pearson correlation coefficient ( $R$ ) of 0.94 for PSA curves (0.2–2.0 s), significantly higher than unconstrained GANs ( $R=0.71$ ) and stochastic simulations ( $R=0.69$ ).
Physical Compliance: 98% of synthetic signals met all three physical constraints simultaneously, compared to only 32% for unconstrained GANs.
Error Metrics: The PSA Root Mean Square Error (RMSE) was 0.12 g (target < 0.15 g), and CAV-RMSE was 0.05 g·s.
Uncertainty Reduction: By augmenting the real catalogue (27 records) with 1,000 synthetic records, the coefficient of variation (CoV) for PSA at $T=1.0$ s was reduced, resulting in a 38% reduction in seismic-hazard uncertainty.
Efficiency: The model eliminated the need for manual post-generation filtering, reducing computational costs by approximately 60% compared to workflows requiring non-physical signal rejection.

Significance and Claims
The paper claims that the pc-cGAN framework bridges the gap between data-driven deep learning and engineering rigor. By ensuring that generated ground motions are not only statistically similar to real records but also physically consistent with ASCE 7–22 and Norma E.030-2018, the model produces inputs directly usable for code-compliant structural design without manual intervention.

The authors highlight the practical significance for Peru, where the generated records enable more accurate probabilistic vulnerability assessments for informal settlements. Specifically, the reduction in hazard uncertainty allows for a shift in risk classification (e.g., from "High Uncertainty" to "Moderate Uncertainty" under ASCE 41–17), potentially preventing unnecessary demolition orders and supporting evidence-based retrofitting policies under the SINAGERD framework. The study concludes that this approach offers a scalable, low-cost solution for seismic risk mitigation in data-scarce regions, though it acknowledges limitations regarding crustal fault zones, spatial correlation, and liquefaction non-linearity, which are identified as targets for future work.