Can AI learn the laws of physics?

Imagine having to solve a super complex mathematical puzzle every time the market changes. For finance experts, calculating option prices is a nightmare: they have to solve incredibly difficult equations that require massive amounts of time and computing power. But what if AI could learn these rules once and for all?

DeepSVM has arrived, a new system using a technology called 'Deep Operator Network.' Unlike standard AI, which learns by looking at thousands of pre-made examples, DeepSVM is different. It doesn't need labeled data; it learns directly by following the laws of physics and mathematics. It's as if, instead of studying old exercises, it learns the fundamental rules of matter to solve any problem on its own!

Thanks to this method, the system is incredibly fast and precise. It can predict prices in real-time, helping to understand market movements. Of course, it's not perfect: it sometimes struggles when changes are too sudden, but it is a giant step toward a future where AI and science collaborate to make everything faster and smarter.

DeepSVM introduces a revolutionary approach in the field of machine learning applied to quantitative finance. The core of the system is the integration of a 'Physics-Informed Deep Operator Network' (PI-DeepONet). Traditionally, stochastic volatility models, such as the Heston model, require solving coupled partial differential equations (PDEs), a computationally expensive process.

The real innovation of DeepSVM lies in the fact that it is not a purely 'data-driven' model. While classical neural networks try to map inputs and outputs based on historical data, DeepSVM uses a 'hard-constrained ansatz.' This means that mathematical laws (such as no-arbitrage conditions and terminal payoffs) are directly embedded into the network's structure. In practice, the AI is not just trying to 'guess' the result, but is forced to respect the laws of financial physics.

To handle the most difficult zones, where changes are sudden and gradients are very high, researchers used 'Residual-based Adaptive Refinement' (RAR). This technique allows the network to focus more on areas where the error is highest, stabilizing the learning process. Although the model is extremely accurate in price calculation, studies have shown that its derivatives (the so-called 'Greeks', used to measure risk) can exhibit noise in critical market zones. This suggests that the next frontier will be the integration of higher-order regularizations to make AI even more precise in subtle mathematical details.