The Role of Physics-Informed Neural Networks (PINNs) in Engineering
Have you ever watched a simulation run—CFD, FEA, heat transfer, electromagnetics—and thought: this is amazing… but also painfully slow? Have you ever had a design question that should be answered in seconds, but instead requires a meshing ritual, solver tuning, and a queue on a shared cluster?
That tension—between fidelity and speed—is one of the most persistent themes in engineering. In an earlier piece, I argued that simulation is one of the “invisible engines” behind modern engineering progress. Introduction. Have you ever won… The story of Physics-Informed Neural Networks (PINNs) fits right into that arc: they’re one of the more compelling attempts to make high-fidelity physics more accessible, more adaptive, and sometimes dramatically faster—especially when data is sparse, geometry is awkward, or we need near real-time answers.
PINNs are not magic. They won’t replace finite element methods or finite volume solvers across the board. But when you understand what they’re good at—and what they struggle with—they become a powerful addition to the engineering toolkit.
What a PINN Really Is (and Why Engineers Should Care)
At a high level, a PINN is a neural network trained to approximate a physical field—temperature, pressure, displacement, velocity, concentration, etc.—while being penalized when it violates the governing physics. In practice, that usually means we embed differential equations (ODEs/PDEs) and boundary/initial conditions directly into the loss function using automatic differentiation.
The core idea became widely known through the foundational work by Raissi, Perdikaris, and Karniadakis, who framed PINNs as neural networks that can solve forward problems (predict the field given the PDE and boundary conditions) and inverse problems (infer unknown coefficients/parameters from limited observations). (Raissi, Perdikaris, and Karniadakis 2019; Raissi, Perdikaris, and Karniadakis 2017). A broader review of “physics-informed machine learning” (PINNs and adjacent approaches) helped clarify where this fits in the wider scientific ML landscape. (Karniadakis et al. 2021).
So why should engineers care?
Because engineering rarely gives us the neat conditions that classical solvers love:
- We may have sparse sensors rather than dense field measurements.
- We may need to infer parameters we cannot measure directly.
- We may need fast surrogate models for design exploration and control.
- We may want to fuse physics + data in a single model rather than choosing one or the other.
PINNs are most compelling in those “messy middle” situations.
PINNs vs. Classical Solvers: A Practical Comparison
Classical numerical simulation (FEM/FVM/FDM)
You discretize the domain (mesh/grid), apply the PDE and boundary conditions, and solve a large system. You get robustness and decades of engineering maturity—but you pay for it in setup time and compute, especially when you need many runs.
PINNs
You avoid explicit meshing (in the traditional sense) and learn a continuous approximation. The “solver” is optimization: you train the network so that the PDE residual is small everywhere it matters, and boundary/initial conditions are satisfied.
This “meshless” quality is often oversold. You still need collocation points (where the PDE residual is enforced), smart sampling, and numerical care. But the workflow can be easier to scale to:
- irregular domains,
- inverse problems,
- multi-fidelity blending,
- and online updates (digital twins).
Where PINNs Shine: The Engineering Use-Cases That Matter
1) Inverse problems and parameter identification
This is one of the most natural wins.
Many real engineering questions are inverse:
- What is the effective diffusivity of a composite?
- What boundary heat flux best explains our sensor readings?
- What material parameters or loads are consistent with observed deflections?
Because the physics is built into training, PINNs can infer parameters with fewer measurements than purely data-driven models—assuming the physics model is appropriate and the data is informative.
Real-world example: batteries. Recent work applies PINNs to identify unknown parameters and simulate electrochemical battery models when parameters are uncertain or not directly measurable. (Wang et al. 2024).
2) Data-scarce environments (the “physics as teacher” effect)
Engineering data is expensive. Sometimes the “dataset” is ten sensors and a handful of operating conditions.
PINNs can be trained with limited labeled data because the PDE residual supplies a strong learning signal. That said, they do not create information out of thin air: if your sensors miss key dynamics, the model can still be underdetermined.
Real-world example: turbulent flow reconstruction with sparse measurements. A pragmatic study on reconstructing turbulent flows using sparse data highlights both promise and limitations—PINNs can assimilate sparse measurements and enforce RANS-based constraints, but cannot recover information that simply isn’t present in the data. (Hanrahan, Kozul, and Sandberg 2023).
3) Digital twins and near real-time prediction
A digital twin is only as useful as its ability to update quickly and answer “what-if” questions under changing conditions.
Here, PINNs are often used as:
- fast surrogates for expensive solvers,
- data assimilation engines that correct a model using sensor data,
- or hybrid models that remain physically consistent while being operationally responsive.
Industrial example: Siemens Energy + NVIDIA (predictive maintenance / digital twin). NVIDIA has described collaborations where physics-informed modeling supports digital twins for power generation equipment—targeting faster inference for maintenance and operational decisions. (NVIDIA 2021b; HPCwire 2021; NVIDIA 2021c).
Industrial example: interactive product design workflows. NVIDIA also published a case where a trained PINN was coupled with a CAD workflow (e.g., Solidworks) to make design iteration more interactive for a product concept (“air knife”). (NVIDIA 2021a).
The important point is not the vendor—it’s the pattern: embed physics, train a surrogate, then deploy it where humans need fast answers.
Real-World Examples Across Domains
Below are a few examples I like because they show the engineering shape of the problem—what’s measured, what’s unknown, and why physics constraints help.
Cardiovascular flows: estimating pressure from non-invasive measurements
A standout applied example uses PINNs with real noisy clinical data to estimate arterial pressure from MRI-derived quantities. This is exactly the kind of inverse problem that’s hard to solve robustly with limited measurements. (Kissas et al. 2020).
Why it matters (beyond medicine): it’s a proof point that PINNs can operate in noisy, real measurement regimes, not just clean PDE benchmarks.
Aerospace structures: near real-time stress prediction
Digital-twin-flavored work has explored PINNs for near real-time stress prediction in aircraft components (e.g., landing gear structures), embedding elasticity equations while producing fast stress estimates as part of a monitoring workflow. (Zhu et al. 2025).
This matters because it aligns with what many teams actually want: fast state estimation under physical constraints, not just a pretty PDE solution.
Manufacturing: thermal history in additive manufacturing
Thermal fields in processes like directed energy deposition can be expensive to simulate repeatedly, but they strongly determine material properties and distortion. PINN-based approaches have been explored to predict thermal history in multi-layer additive manufacturing contexts. (Peng et al. 2024).
Why it matters: the process is dynamic, multi-physics adjacent, and operationally relevant.
Energy systems: monitoring industrial heat exchangers
There’s also growing work on PINN-style models for real-time monitoring of heat exchangers—systems where boundary conditions change, sensors are limited, and fast inference can be valuable for efficiency and predictive maintenance. (Majumdar et al. 2022; Majumdar et al. 2025).
The Part People Skip: Why PINNs Can Be Hard to Train
PINNs are often introduced with elegant diagrams and tidy loss functions. In practice, the training can be the entire battle.
Some known pain points:
Gradient pathologies and loss balancing
PINNs frequently combine multiple objectives: PDE residuals, boundary conditions, initial conditions, and data misfit. These terms can have very different scales and optimization dynamics.
A widely cited paper by Wang, Teng, and Perdikaris analyzes “gradient flow pathologies” in PINNs and proposes strategies to mitigate them. (Wang, Teng, and Perdikaris 2021).
Stiff PDEs and multiscale behavior
Stiffness and sharp features (boundary layers, discontinuities, high-frequency content) can cause optimization to stall or converge to trivial/incorrect solutions.
There is active work on strategies for stiff PDE regimes and training stability. (Sharma et al. 2023).
Turbulence and “physics mismatch”
If your physics model is incomplete or too simplified (for example, turbulence closures that don’t match reality), the PINN may dutifully satisfy the wrong constraints. In turbulence settings, researchers have emphasized that PINNs are not a substitute for missing information. (Hanrahan, Kozul, and Sandberg 2023).
What Engineers Are Doing About It
This is where the field has been moving quickly—less “PINNs solve everything,” more engineering-informed training strategies:
- Adaptive sampling / refinement: focus collocation points where residuals are large. (Lu et al. 2021).
- Self-adaptive weighting: learn weights so the model focuses on hard regions. (McClenny and Braga-Neto 2023).
- Better normalization / nondimensionalization: reduce scale imbalance (a deceptively big deal in practice). (Kissas et al. 2020).
- Hybrid approaches: couple PINNs with reduced-order models, classical solvers, or data-driven surrogates.
- Tooling: libraries and platforms have made PINNs more reproducible and accessible—e.g., DeepXDE in academia (Lu et al. 2021), and engineering-oriented frameworks like NVIDIA PhysicsNeMo/Modulus in industry contexts. (NVIDIA n.d.; NVIDIA 2021b).
Where I Think PINNs Fit in an Engineering Organization
If you’re deciding whether PINNs are worth investing in, I’d frame it like this:
PINNs are most valuable when…
- You have some physics you trust, but not enough data for pure ML.
- You have some data, but not enough to calibrate or validate a full solver repeatedly.
- You need fast inference for monitoring, control, or design iteration.
- You care about physical consistency as a constraint, not a post-processing check.
PINNs are not the right hammer when…
- You already have a robust solver and you only need a handful of runs.
- The physics is unknown or dominated by effects you cannot model.
- You need certified accuracy in regimes where PINNs are not yet stable (e.g., strongly turbulent, high-Re flows) and cannot tolerate training fragility.
The best teams I’ve seen treat PINNs as complementary:
- classical solvers for truth/high-fidelity,
- PINNs for fast surrogates, inverse problems, and data assimilation,
- and good engineering judgment to connect the two.
PINNs in the Age of Generative AI
Over the last couple of years, “Generative AI” has gone from a novelty to a serious interface layer for knowledge work. In engineering, though, the story is more nuanced.
If you’re writing code, drafting specs, or summarizing test reports, today’s generative models can already be helpful. But if you’re asking a model to design a bracket, optimize a heat sink, or propose a flow path that won’t cavitate—engineering reality shows up fast. Geometry, constraints, manufacturability, safety factors, standards, tolerances, multi-physics coupling… it’s not enough to generate something that looks plausible. It has to work.
That’s where physics-informed approaches (including PINNs) matter in a generative era: they’re part of the bridge between language-level plausibility and engineering validity.
Why “generative” alone isn’t enough for engineering
Generative models are extremely good at learning patterns in data. But engineering is full of “pattern-shaped traps”:
- A design can look right and still fail on fatigue.
- A pressure field can look smooth and still violate conservation laws.
- A control policy can look stable and still destabilize under a regime change.
In other words: engineers don’t just need creativity. We need constraints, consistency, and verifiability.
PINNs (and, more broadly, physics-informed ML) offer a structured way to bring those requirements into the learning loop. Even when a model is generating candidate solutions, physics-informed components can act as:
- a critic (reject designs that violate basic physics),
- a guide (push search toward feasible regions),
- an accelerator (fast surrogates for repeated simulation),
- an inverse engine (infer hidden parameters from sparse signals).
This is what makes the combination of generative AI + physics-informed learning interesting. It isn’t “GenAI replaces simulation.” It’s closer to: GenAI proposes; physics-informed models filter, refine, and ground; classical solvers validate.
The workflow shift: from “one design per week” to “dozens per day”
If you look at the bottleneck in many engineering organizations, it’s not that people can’t think of ideas. It’s that the feedback loop is slow.
A typical loop looks like:
- propose design change
- mesh / set up physics
- run solver
- post-process results
- decide next move
That loop can take hours or days. So you get fewer iterations. Fewer iterations tends to mean more conservative design decisions, longer timelines, and more reliance on experience and intuition (which is not a bad thing—but it’s expensive and doesn’t scale).
The next decade of engineering AI, in my view, is all about compressing that loop.
Generative AI can help with the “proposal” step—generating candidate geometries, parameter sets, or design concepts. PINNs and physics-informed surrogates can help compress steps (2)–(4) into something closer to real-time. That combination is what turns generative AI from “cool demos” into an actual design amplifier.
Where this is heading
I’ll be direct: I don’t think the final form of “engineering GenAI” is a chat interface that spits out a finished design and calls it a day.
I think the mature version looks more like:
- a design co-pilot that understands constraints,
- can propose options across a multi-objective space (mass, cost, thermal, stress, efficiency),
- uses physics-informed surrogates to evaluate and refine quickly,
- and knows when to escalate to high-fidelity simulation or testing.
And importantly: it keeps a traceable path from assumptions → constraints → evaluations → validation.
That’s how engineers build trust.
Ren Ai: building generative AI that engineers can actually use
This is exactly the direction we’re taking at Ren Ai. We’re building the next generation of Generative AI for engineering design, with the goal of enabling fast iteration without losing the rigor that engineering demands.
In practice, that means integrating:
- generative models for proposing and exploring designs,
- physics-informed learning (including PINN-style methods) for rapid, constraint-aware evaluation and parameter inference,
- and the ability to plug into classical solvers when high-fidelity validation is required.
The vision is not to replace engineering. It’s to increase the number of meaningful iterations an engineer can run, and to make the design space more searchable, more testable, and more responsive to constraints.
A realistic timeline: 2026–2030 for meaningful maturity
If you ask me when this becomes truly useful at scale—when a “generative engineering assistant” moves from novelty to a meaningful tool engineers rely on—I think the window is somewhere between 2026 and 2030.
That’s not a prediction carved in stone; it’s a practical read of what needs to mature:
- better physics-grounded evaluation loops,
- more robust training for difficult PDE regimes,
- better integration with CAD/CAE workflows,
- more trustworthy uncertainty estimates,
- and organizational comfort with AI-in-the-loop design decisions.
The upside is large: faster cycles, broader exploration, earlier detection of infeasible directions, and better use of scarce simulation and test resources. The hard part is building systems that behave like engineering tools—reliable, testable, and grounded—rather than like impressive demos.
Looking Ahead: PINNs as a Bridge Technology
PINNs sit at an interesting intersection:
- They inherit the discipline of physics-based modeling,
- while taking advantage of the flexibility and deployment patterns of ML.
As digital twins become more common, and as organizations demand models that update from real data rather than living as static “analysis artifacts,” I expect physics-informed learning to show up more—not necessarily as “a PINN everywhere,” but as a set of ideas embedded into engineering workflows.
The practical future, in my view, looks like:
- PINN-style surrogates around expensive simulations,
- physics-informed assimilation layers on top of sensor streams,
- and hybrid pipelines where we stop pretending the choice is either physics or data.
It’s both. And engineering has always lived in the “both.”
References
Hanrahan, S., M. Kozul, and R. D. Sandberg. 2023. “Studying Turbulent Flows with Physics-Informed Neural Networks and Sparse Data.” International Journal of Heat and Fluid Flow 101: 109232.
HPCwire. 2021. “Nvidia Digital Twins Power Predictive Maintenance for Siemens Energy.” November 15, 2021.
Karniadakis, George E., Ioannis G. Kevrekidis, Lu Lu, Paris Perdikaris, Sifan Wang, and Liu Yang. 2021. “Physics-Informed Machine Learning.” Nature Reviews Physics 3 (6): 422–440.
Kissas, Georgios, Yibo Yang, Eileen Hwuang, Walter R. Witschey, John A. Detre, and Paris Perdikaris. 2020. “Machine Learning in Cardiovascular Flows Modeling: Predicting Arterial Blood Pressure from Non-Invasive 4D Flow MRI Data Using Physics-Informed Neural Networks.” Computer Methods in Applied Mechanics and Engineering 358: 112623.
Lu, Lu, Xuhui Meng, Zhiping Mao, and George E. Karniadakis. 2021. “DeepXDE: A Deep Learning Library for Solving Differential Equations.” SIAM Review 63 (1): 208–228.
Majumdar, R., et al. 2022. “Real-Time Health Monitoring of Heat Exchangers using Physics-Informed Neural Networks.” NeurIPS Workshop on Machine Learning and the Physical Sciences (ML4PS).
Majumdar, R., et al. 2025. “HxPINN: A Hypernetwork-Based Physics-Informed Neural Network Model for Real-Time Monitoring of an Industrial Heat Exchanger.” Numerical Heat Transfer, Part B: Fundamentals.
McClenny, Levi D., and Ulisses Braga-Neto. 2023. “Self-Adaptive Physics-Informed Neural Networks.” Journal of Computational Physics 474: 111722.
NVIDIA. n.d. “NVIDIA PhysicsNeMo.” Accessed 2026-01-28.
NVIDIA. 2021a. “Accelerating Product Development with Physics-Informed Neural Networks and Modulus.” November 2, 2021.
NVIDIA. 2021b. “NVIDIA Announces PhysicsNeMo (Previously SimNet), a Framework for Developing Physics-ML Models for Digital Twins.” November 9, 2021.
NVIDIA. 2021c. “Siemens Energy Taps NVIDIA to Develop Industrial Digital Twin of Power Plants.” November 15, 2021.
Peng, B., et al. 2024. “Multi-Layer Thermal Simulation Using Physics-Informed Neural Networks for Directed Energy Deposition.” Additive Manufacturing 79: 103905.
Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. 2017. “Physics Informed Deep Learning (Part I): Data-Driven Solutions of Nonlinear Partial Differential Equations.” arXiv:1711.10561.
Raissi, Maziar, Paris Perdikaris, and George E. Karniadakis. 2019. “Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations.” Journal of Computational Physics 378: 686–707.
Sharma, Prakhar, Llion Evans, Michelle Tindall, and Perumal Nithiarasu. 2023. “Stiff-PDEs and Physics-Informed Neural Networks.” Archives of Computational Methods in Engineering.
Wang, J., et al. 2024. “A Physics-Informed Neural Network Approach to Parameter Identification and Simulation of Electrochemical Battery Models.” Journal of Power Sources 621: 235271.
Wang, Sifan, Yujun Teng, and Paris Perdikaris. 2021. “Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks.” SIAM Journal on Scientific Computing 43 (5): A3055–A3081.
Zhu, Z., et al. 2025. “Physics-Informed Machine Learning for Near Real-Time Stress Prediction on an Aircraft Landing Gear Component.” Engineering Applications of Artificial Intelligence.