Physics-Informed State Space Models for Reliable Solar Irradiance Forecasting in Off-Grid Systems

Physics-Informed State Space Models (PISSMs) improve solar irradiance forecasting by integrating atmospheric thermodynamics into deep learning. This approach resolves critical anomalies like temporal lags and physical inconsistencies, ensuring more reliable energy management in off-grid photovoltaic systems.

intermediate1 hour5 steps

The play

Understand Physics-Informed ML Foundations
Grasp the core concept of integrating domain-specific physical laws directly into machine learning models to enhance robustness and interpretability.
Identify Key Physical Principles
Pinpoint relevant atmospheric thermodynamics equations, conservation laws, or physical bounds crucial for accurately modeling solar irradiance behavior (e.g., energy balance, cloud dynamics).
Translate Physics to Model Constraints
Formulate these physical laws into mathematical terms (e.g., differential equations, inequalities, or penalty functions) suitable for regularization or direct integration within an ML framework.
Architect a PISSM
Design a neural network architecture or a custom loss function that incorporates both data-driven learning from sensor data and the physics-based constraints identified in previous steps.
Train and Validate Your PISSM
Train the Physics-Informed State Space Model using real-world solar irradiance data. Rigorously validate its performance, ensuring it not only achieves high forecasting accuracy but also maintains physical consistency, especially during cloud transients, for reliable off-grid system operation.

Starter code

import torch
import torch.nn as nn

def simple_physics_constraint(predicted_irradiance):
    """
    A simplified physics-based constraint for solar irradiance.
    Penalizes negative irradiance or values exceeding a physical maximum.
    In a full PISSM, this would involve more complex atmospheric thermodynamics.
    """
    negative_penalty = torch.relu(-predicted_irradiance) # Irradiance cannot be negative
    max_irradiance_limit = 1500 # W/m^2, approximate max solar irradiance
    excess_penalty = torch.relu(predicted_irradiance - max_irradiance_limit)
    return torch.mean(negative_penalty + excess_penalty)

class PhysicsInformedLoss(nn.Module):
    """
    Custom loss function combining a data-driven MSE with a physics-based penalty.
    """
    def __init__(self, lambda_physics=0.1):
        super().__init__()
        self.mse_loss = nn.MSELoss()
        self.lambda_physics = lambda_physics

    def forward(self, predictions, targets):
        data_loss = self.mse_loss(predictions, targets)
        physics_loss = simple_physics_constraint(predictions)
        total_loss = data_loss + self.lambda_physics * physics_loss
        return total_loss

Source

Paperarxiv.org