Physics Informed Neural Networks (PINNs)

What are PINNs?

OriGen is leading the revolution in a new frontier of artificial intelligence (AI) algorithms to solve partial differential equations (PDEs), and making the impossible possible: enabling complex physical simulations 10,000x  faster than traditional technology.

Traditional simulation technologies for the physical processes that define our world are computationally expensive, and force significant compromises, greatly limiting scope, scale, and breadth of analysis.

OriGen has pushed the boundaries, addressing the fundamental question of which network architectures are best suited to learn the complex behavior of nonlinear PDEs. We combine proprietary neural network architectures in addition to calculating and minimizing the residual.

This new simulation technology runs up to 10,000x faster than conventional numerical simulators  and has the ability to connect to any optimizers, enabling users to make better decisions, reduce uncertainty and improve success rates.

The range of applications is extraordinary, from the simulation of reservoirs, geothermal energy, to CO2 sequestration and hydrogen storage, practically, any physical process governed by differential equations can be simulated using this approach.

As this is an entirely new approach to simulation, understanding the details behind it also require some new concepts. A core concept, is that neural networks can approximate the solution of differential equations, and in particular, high-dimensional partial differential equations (PDEs). One of the most promising approaches to efficiently solve these non-linear PDEs is Physics-Informed Neural Networks (PINNs). These PINNs are trained to solve supervised learning tasks constrained by PDEs, such as the conservation laws in continuum theories of fluid and solid mechanics. The idea behind PINNs is to train the network using automatic differentiation (AD) by calculating and minimizing the residual (the error of solving the PDE), usually constrained by initial and boundary conditions.

This paper provides a good introductory overview of PINNs with respect to a well known industry problem (Buckley Leverett):

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