Mahdi Nasiri Abarbekouh

Modeling complex physical systems for industrial and scientific applications

presents a significant challenge due to the limitations of existing approaches.

First-principles models often struggle with systems that are too complex, partially

unknown, or computationally expensive to simulate accurately. Meanwhile,

purely data-driven machine learning models require large amounts of

high-quality data, lack physical interpretability, and frequently fail to generalize

beyond their training distribution, especially with sparse or noisy

datasets. These limitations create a critical need for a methodology that

leverages the complementary strengths of both approaches.

This research focuses on physics-informed machine learning (PIML), an approach

that integrates known physical knowledge—expressed through governing

equations, conservation laws, and domain constraints—directly into

the learning process of machine learning models.

The PIML framework delivers robust generalization by producing physically

plausible and interpretable results with superior extrapolation capabilities

compared to purely data-driven methods. It also achieves significantly

greater data efficiency, enabling accurate predictions even with sparse, noisy,

or limited datasets.

Existing solutions remain divided between first-principles modeling and purely

data-driven machine learning. PIML, by using both physical knowledge and

data-driven learning, establishes a sophisticated framework for scientific machine

learning that outperforms traditional methods in reliability, efficiency,

and applicability.