Let the ML learn physics

Multi-physics simulations have been traditionally using numerical methods to solve Partial Differential Equations (PDE).

Most of the time real-life physical problems give many surprises with noisy boundary conditions & missing data.

We need to manage the data to strike a balance somewhere.

PDEs can't incorporate noisy/multi fidelity data & nor can they tackle high-dimensional problems, let alone meshing complexities.

On the other hand, IoT is leaping forward towards a trillion sensors by the next decade. We are ill-equipped to embedd such multi-fedilty data seemlessily into existing physical models.

The wealth & spatiotemporal heterogeneity of data has no universally acceptable models yet. Here comes machine learning for rescue. DL techniques pull out essential features out of a pile of data. Yet, it stumbles to extract interpretable information & knowledge out of them.

Purely data-driven ML models optimize data efficiently, with advanced algorithms. Still many of the predictions are inconsistent/ implausible.

What if, ML learns physics & applies  it?

The neurals can be trained with physical laws & domain knowledge so that "informative priors" influence the noisy real-life data to be interpreted with "sense".

Now, another problem pops out. The machine learning techniques need a large amount of data for training. There are cases which has only data from the boundary conditions. At the other end, there are lots of data available with little physics. These two scenarios can be ignored here.

However, the majority of real applications fall in between. Partially known physics with scattered data are abundantly present. Physics trained ML helps find missing functional terms in PDEs.

Also there are many problems involving long-range spatiotemporal interactions such as turbulence & visco-elasto-plastic materials or other anomalous transport properties that can be solved with physics based ML.

These kinds of physical problems lack data which can be obtained by solving PDEs.

Thus numerical methods and neural networks can be designed to be interlinked to obtain informative priors.

With this approach, ML learns physics & applies accordingly.

Thus wedding numerical methods with neural networks paves path to the new approach of getting deep insights of physical phenomena.

Let ML learn physics.

Image & Reference; https://t.co/oaqwME6Gxq

#physics
#MachineLearning
#NeuralNetwork