How does loss functions work in PINN? [D]

2026-05-19 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning · Depth: Intermediate, quick

Summary

A user learning Physics-informed Neural Networks (PINNs) inquired about how weighted loss functions influence model predictions, specifically when the total loss value can be achieved through multiple combinations of individual loss components and their respective lambda weights. The core question addresses how a neural network discerns which loss components are prioritized for correction during training, given that the total loss is a single numeric value. Responses clarified that the training process relies on the gradient of the loss function, not its absolute value. The coefficients (lambdas) determine the sensitivity of the training to changes in each loss component, and gradient descent prioritizes adjustments that lead to the largest reduction in the overall weighted loss.

Key takeaway

For Machine Learning Engineers optimizing PINNs or similar multi-objective models, you should understand that the network learns by minimizing the gradient of the total loss, not its absolute value. Your chosen lambda coefficients directly determine how sensitive the training process is to changes in each individual loss component. Carefully tune these weights to guide gradient descent towards desired physical or initial condition adherence.

Key insights

Neural networks learn from loss function gradients, not absolute values, with coefficients shaping training sensitivity.

Principles

• Training optimizes loss gradients.
• Coefficients dictate loss component influence.

Method

Backpropagation and Stochastic Gradient Descent (SGD) use loss gradients across batches to signal network improvements, with explicit weights determining each term's influence.

In practice

• Adjust lambda values to control training sensitivity.
• Focus on gradient behavior, not just total loss magnitude.

Topics

• Physics-Informed Neural Networks
• Loss Functions
• Backpropagation
• Gradient Descent
• Hyperparameter Optimization

Best for: Machine Learning Engineer, AI Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.