Learn how Physics-Informed Neural Networks are accelerating simulations, improving accuracy, and unlocking new possibilities in engineering and beyond

In the world of AI, a lot of development is research-driven, constantly seeking new ways to model and understand complex systems. One such breakthrough is Physics-Informed Neural Networks (PINNs), a revolutionary approach that integrates deep learning with physics-based modeling, unlocking unprecedented accuracy and efficiency in scientific computing and engineering applications.

What is PINNs (Physics-Informed Neural Networks) ?

Physics-Informed Neural Networks (PINNs) are a special type of neural network that incorporate physical laws directly into their design. This means they learn not only from data but also from the physics that govern the problem.

Traditional AI models often act like “black boxes,” making it hard to understand how they make decisions. In contrast, PINNs use physics equations, ensuring their results follow known physical principles. This makes their outputs more understandable and reliable.

What Difference between PINNs Model and Traditional Surrogate Model ?

There is several points difference between surrogate model with and without PINNs, let’s discuss it :

• Learning Approach : Traditional surrogate model approach primarialy learn from dataset. They act as “black boxes” that can make predictions but often lack interpretability. The opposite, PINNs integrate physical laws directly into their architecture, they learn not only from data but also from the underlying physics geverning equations of the problem.
• Accuracy and Reliability : Traditional surrogate model accuracy depends heavily on the quality and quantity of the training data. They may struggle with extrapolation beyond the training data range. PINNs By incorporating physics equations, PINNs ensure that their predictions adhere to known physical principles, making their outputs more reliable and interpretable
• Dataset Requirements : Traditional surrogate model eequire large amounts of high-quality data for training. The opposite, PINNs while they also require data, the integration of physical laws can reduce the dependency on large datasets. This make them more efficient when only have small dataset but the physcial laws are well understood.
• Application Scope : Traditional surrogate model commonly used in various fields like engineering, finance, and healthcare for tasks such as optimization and prediction. While PINNs only useful in fields where physical laws are well-defined, such as fluid dynamics, structural mechanics, and thermodynamics. Excel in solving partial differential equations (PDEs) and related physics-based problems only.

In summary, while traditional surrogate models rely heavily on data and can be less interpretable, PINNs leverage both data and physical laws to provide more accurate, reliable, and interpretable results, especially in physics-based applications.

The Advantage of Physics-Informed Neural Networks

Beside, the advantage that already mentions above, there is other advantage of PINNs like :

• Robustness and Generalization, because they are grounded by physical laws, PINNs better at generalizing to new and unseen scenarios. This make them more robust and reliable when applied difference problem with simillar physical domain
• Enhanced Predictive Power, with the initial physical insights, PINNs can capture complex behaviors that purely data-driven models might miss. This enhances their predictive power and makes them valuable for advanced simulations and predictions.
• Interpretability, AI models often lack transparency, making it difficult to understand how they arrive at their predictions. PINNs on the other side have their adherence to physical laws provides a clear framework for understanding their predictions, enhancing interpretability and trustworthiness.
• Reduced Data Requirements,  by leveraging physical laws, PINNs can achieve high accuracy with less data compared to traditional models.

Nothing is perfect: The Challange of using PINNs

• High Computational Demand: PINNs often require significant computational resources, especially when dealing with high-order derivatives and complex physical laws. This can make training and implementation more resource-intensive compared to traditional models.
• Very Limited Convergence Theory: The theoretical understanding of PINNs’ convergence is still developing. This means that ensuring consistent and reliable performance across different problems can be challenging.
• Training Complexity: There is a lack of unified training strategies for PINNs. Developing effective methods to train these networks efficiently and accurately remains an ongoing area of research.
• Handling Complex Systems: While PINNs excel in many scenarios, they can struggle with highly complex and non-linear systems. Their performance may not always be optimal in such cases.
• Dataset Scarcity and Quality: Although PINNs can work with limited data, the quality and relevance of the data are crucial. Poor or noisy data can still impact the accuracy and reliability of the model.
• Numerical Stability in Training: Maintaining numerical stability during training can be challenging, particularly when dealing with high-frequency and multiscale components of physical systems.

Despite these challenges, ongoing research and advancements in the field are continually improving the capabilities and robustness of PINNs. As the technology evolves, many of these limitations are expected to be addressed, making PINNs an even more powerful tool for solving complex physical problems.

NVIDIA Modulus, Package to develop Physics-Informed Neural Networks

NVIDIA Modulus is an open-source framework designed to build, train, and fine-tune Physics-Informed Neural Networks (PINNs). These networks combine physics-driven causality with simulation and observed data to solve complex problems in various domains, such as computational fluid dynamics, structural mechanics, and electromagnetics.

We make a report about NVIDIA Modulus, you can read our report in this post A report on PINNs surrogate model is now released.

Our Own development PINNs Models – by Astraea Software

NVIDIA Modulus has its limitations, leaving several equations and constraints uncovered, there is still a wide range of physics simulation available that not cover by NVIDIA Modulus. At Astraea Software, we have developed our own Physics-Informed Neural Networks (PINNs) models to address the limitations of existing solutions like NVIDIA Modulus. We can add and modify things like :

• Customize and write our own PDEs for specific simulations by ourself or costomer request.
• Define unique training constraints.
• Modify the PINNs training architecture pipeline to meet our needs.

Depend on the simulation requirement, define the training constrain and others aspect that not covered by NVIDIA Modulus Package. We make a report about our own PINNs model that we modify from NVIDIA Modulus, you can read our report in Here.

How We Apply NVIDIA Modulus

We as Pionner in 3D AI Technology in manufacuring technology do some research in NVIDIA Modulus for PINNs and try to make real application using NVIDIA Modulus in real simulation condition, with purpose to enrich our insight about PINNs and build some contribution to the engineer world.

With several trial and modification, we can get resonable result on PINNs that reported in our product page, click button below to access it.