PINA: artificial intelligence accelerating scientific simulation
The open-source library developed at SISSA in Trieste becomes a strategic asset for Spoke 9
In the world of mathematical modeling and numerical simulation, a heartbeat can last an eternity—literally. Simulating such a fast and dynamic event may require up to an entire day of computation when using traditional methods to solve partial differential equations (PDEs). These are mathematical equations that describe complex phenomena such as fluid flow, material behavior, or human physiology. PDEs are essential tools in fields like fluid dynamics, biomechanics, and aerodynamics, but solving them numerically is extremely demanding in terms of time and computational resources.
An effective response to this challenge comes from SISSA – the International School for Advanced Studies in Trieste. It’s called PINA, an open-source Python library designed for the efficient simulation of complex systems. PINA, which stands for Physics-Informed Neural networks for Advanced modeling, is the result of research carried out by the SISSA mathLab group and is freely available on GitHub under the MIT license.
Artificial intelligence at the service of physics
PINA’s goal is to merge mathematical models with deep learning, a branch of artificial intelligence that uses deep neural networks—structures composed of many interconnected layers—to analyze and learn complex patterns. In particular, the library enables the construction of physics-informed neural networks (PINNs), which are capable of learning the physical laws governing real-world systems and solving the corresponding PDEs even in the absence of simulation data.
At the core of PINA’s philosophy lies the concept of surrogate modeling: the creation of simplified mathematical models that replicate the behavior of physical systems while drastically reducing computation time, without significantly compromising accuracy. This approach follows an offline-online decomposition, where the computationally intensive offline phase involves gathering high-fidelity simulation data (when available) and building the surrogate model. The lightweight online phase then leverages this model to produce fast, near real-time simulations.
Thanks to its modular and scalable architecture, PINA supports both automated usage for those seeking simplicity and advanced customization for users who want full control over the simulation workflow.
A strategic tool for Spoke 9
PINA is emerging as a key enabling technology within Spoke 9 of the iNEST Consortium, which focuses on models, methods, and computational tools for the development of Digital Twins. The software incorporates model order reduction techniques (Research Topic 2) to simplify complex simulations while preserving accuracy and integrates machine learning to enable adaptive features in digital twin systems (Research Topic 3). Moreover, PINA is designed for practical applications across a wide range of sectors—from biomedicine to advanced manufacturing (Research Topic 4).
During the 2025 edition of the YMMOR conference, hosted at SISSA, PINA was featured in a hands-on tutorial attended by over 30 early-career researchers from across Europe. Participants had the opportunity to use the library to build models capable of simulating real-world problems, further demonstrating PINA’s effectiveness not only as a scientific tool but also as a high-level educational resource.
Bridging research and the future of Northeastern Italy
The PINA ecosystem continues to expand, supported by an increasingly active and international community. Its rapid growth suggests a promising future as a reference platform in the field of scientific machine learning, uniquely positioned to integrate AI with computational science and applied mathematics at a deep level.
As Northeastern Italy invests in digital innovation and the development of Digital Twins as strategic tools, technologies like PINA stand out as foundational infrastructures—true enablers of digital transformation.