Physics-Informed Neural Networks: Bridging mathematical physics with deep learning architectures.

Why hardcoding physical laws into neural network loss functions is solving deep learning's biggest flaw in science and engineering.

Over the past decade, deep learning has achieved unmatched success in image recognition, natural language processing, and generative media. These conventional models are purely data-driven: they ingest millions of data points, learn statistical correlations, and predict outputs based entirely on pattern matching.

However, when applied to physical sciences such as aerodynamics, climate modeling, structural engineering, or fluid dynamics purely data-driven neural networks hit a major wall: they do not know the laws of physics.

A standard neural network trained on fluid velocity data might produce a visually convincing prediction that secretly violates the conservation of mass or energy.…