When we think of artificial intelligence, we often imagine machines that learn by consuming enormous amounts of data—reading text, recognizing images, or predicting patterns purely from examples. Large Language Models (LLMs), for instance, learn language by absorbing vast libraries of written text and identifying statistical relationships between words. Their intelligence is impressive, but it is also fundamentally data-driven.
Now imagine an AI model that does not merely learn from data, but is forced to obey the laws of nature while learning. Such a model cannot invent physically impossible answers, even when data are scarce or incomplete. This is the idea behind Physics-Informed Neural Networks, or PINNs.
PINNs belong to a unique class of machine-learning models that blend data with governing physical laws—such as equations describing fluid motion, heat transfer, or structural dynamics. Rather than memorizing examples, these models learn by balancing observations with constraints imposed by physics. This makes them especially attractive for scientific and engineering problems where measurements are limited, expensive, or noisy.
In aerodynamics, PINNs hold enormous promise. They can solve both forward problems (predicting flow given conditions) and inverse problems (recovering hidden quantities such as pressure or forces from limited data). However, PINNs also face serious challenges. They are notoriously difficult to train, particularly for unsteady flows involving moving or flapping bodies, where the shape of the domain itself changes with time. Traditional PINNs often struggle or fail outright in such situations.
Earlier work addressed part of this challenge by introducing an immersed boundary–aware (IBA) framework for PINNs. This framework allows neural networks to operate on a fixed background grid while still accounting for moving boundaries—much like the immersed boundary methods used in computational fluid dynamics. Two formulations were proposed: one based on the standard Navier–Stokes equations (MB-PINN), suitable when body motion is known, and another based on immersed boundary formulations (MB-IBM-PINN), capable of handling cases where body position or velocity is unknown.
Yet an even deeper challenge remained—time.
Unsteady flow problems often require resolving dynamics over long time horizons. PINNs, however, do not train well over long temporal domains. Errors accumulate, gradients vanish, and predictions degrade rapidly. This temporal fragility severely limits their usefulness for realistic aerodynamic systems.
To overcome this, the present study introduces sequential learning strategies tailored for physics-informed neural networks. Two approaches were explored. The first, time marching, gradually increases the time domain during training. The second, time-domain decomposition, splits the temporal domain into smaller segments and trains the model sequentially, transferring learned knowledge between segments.
The results are clear. Time-domain decomposition, especially when combined with transfer learning and physics-guided sampling, dramatically improves both accuracy and computational efficiency. This approach enables reliable recovery of pressure fields and aerodynamic loads—even in flows with complex, quasi-periodic behaviour—where standard PINNs fail.
While the present work focuses on a single flow configuration, it opens the door to far broader possibilities. Future extensions could incorporate operator learning, enabling models that generalize across many flow conditions, such as varying wing motions or gusty inflows.
In essence, this research shows that making neural networks respect physics is not enough. How they learn in time matters just as much—and with the right strategies, PINNs can become powerful, reliable tools for understanding the physics of flight, recovering missing physics and observations.
The following are the authors of this paper:
- Mr. Rahul Sundar from the Department of Aerospace Engineering, Indian Institute of Technology (IIT) Madras, Chennai, India.
- Dr. Didier Lucor from Laboratoire Interdisciplinaire des Sciences du Numérique LISN-CNRS, Orsay, France.
- Prof. Sunetra Sarkar from the Department of Aerospace Engineering, Indian Institute of Technology (IIT) Madras, Chennai, India.
Article by Akshay Anantharaman
Click here for the original link to the paper
