Nazanin Ahmadi, Qianying Cao, Jay D. Humphrey, George Em Karniadakis
5 min
Physics-informed machine learning (PIML) is emerging as a potentially transformative paradigm for modeling complex biomedical systems by integrating parameterized physical laws with data-driven methods. Here, we review three main classes of PIML frameworks: physics-informed neural networks (PINNs), neural ordinary differential equations (NODEs), and neural operators (NOs), highlighting their growing role in biomedical science and engineering. We begin with PINNs, which embed governing equations into deep learning models and have been successfully applied to biosolid and biofluid mechanics, mechanobiology, and medical imaging, among other areas. We then review NODEs, which offer continuous-time modeling, especially suited to dynamic physiological systems, pharmacokinetics, and cell signaling. Finally, we discuss deep NOs as powerful tools for learning mappings between function spaces, enabling efficient simulations across multiscale and spatially heterogeneous biological domains. Throughout, we emphasize applications where physical interpretability, data scarcity, or system complexity make conventional black-box learning insufficient. We conclude by identifying open challenges and future directions for advancing PIML in biomedical science and engineering, including issues of uncertainty quantification, generalization, and integration of PIML and large language models.
Physics-Informed Machine Learning (PIML) represents a paradigm shift in biomedical science and engineering by bridging the gap between data-driven modeling and fundamental physical principles. Traditional black-box machine learning often struggles with data scarcity and lack of interpretability in complex biological systems. PIML addresses these issues by embedding governing physical laws—such as mass, momentum, and energy conservation—directly into the loss functions or architectures of neural networks. This integration ensures that model predictions remain physically consistent, even when training data is sparse or noisy.
The authors review three foundational classes of PIML frameworks:
The ability to synthesize experimental data with mechanistic knowledge allows researchers to move beyond simple correlation-based models. PIML enables the discovery of hidden biological mechanisms, facilitates personalized medicine through patient-specific digital twins, and reduces the reliance on computationally expensive numerical simulations. As the field matures, the integration of PIML with foundation models and large language models (LLMs) promises to automate complex modeling workflows, potentially accelerating scientific discovery and clinical decision-making.
Alex: [precise] That's the intended behavior. And the paper gives a concrete example of how far you can push this. They discuss the Peridynamic Neural Operator — the PNO — which goes further than just a penalty term in the loss. It embeds nonlocal mechanics directly into the architectural design. The assumption is that material points interact within a defined neighborhood, and that lets you hard-code Galilean invariance and momentum balance into the operator itself rather than hoping the network learns them from data.
Sam: [leaning in] So the physics is structural, not just a soft constraint. Does that actually move the needle on real tissue data?
Alex: [measured, confident] Substantially, on the one test case they report in detail. On porcine tricuspid valve leaflets, the PNO reduced prediction errors by roughly three-quarters compared to models that didn't account for heterogeneous fiber orientation. It also inferred stress fields that weren't directly present in the original imaging — which is the kind of extrapolation you'd need for surgical planning.
Sam: [reflective] That's a meaningful reduction. Though I'd want to know how that generalizes beyond one tissue type and one imaging protocol. [[RP_SECTION:limitations-and-future-challenges|Limitations and Future Challenges]]
Alex: [slower, deliberate] That's the right instinct, and the review is candid about the open problems. Two stand out. First, the governing equation quality problem: if your physical model is misspecified, you encode that error into the network, and there's no data-driven mechanism to correct a structurally wrong prior. Second, the optimization landscape. These models are prone to spectral bias — they preferentially learn low-frequency components — and they struggle to converge on stiff, multiscale biological equations. The authors flag curriculum learning as a partial mitigation, but it requires careful tuning and isn't a solved problem.
Sam: [nodding] And I'd add uncertainty quantification to that list. If these models are going to inform clinical decisions, you need calibrated confidence estimates, not just point predictions.
Alex: [confirming] The review flags UQ as an active area of development — which is a polite way of saying the field doesn't have a satisfying answer yet. That's probably the sharpest limitation for clinical translation. A model that gives you a prediction without a reliable uncertainty bound is difficult to act on responsibly.
Sam: [processing] So the honest summary is: the architectural ideas are well-motivated and the early results on specific tasks are encouraging, but the path from a validated operator on one tissue type to a deployable clinical tool involves several unsolved problems.
Alex: [concluding with quiet confidence] That's a fair read of where the field sits. The hybrid approach — physical structure combined with data-driven flexibility — is a meaningful step beyond either pure mechanistic modeling or unconstrained deep learning. But the review is making a case for a research direction as much as reporting a solved problem. The value is in knowing which constraints to embed and where to let the data speak, and that judgment still requires deep domain knowledge. You can't substitute physics for understanding the system.
Sam: Thanks for listening to ResearchPod.