The word AI has become a household word. Now that OpenAI’s interpretive large language model Chat-GPT (Financed and supported by Microsoft) is being used/misused for everything from writing essays, legal documents, for generating mathematical proofs and even telling jokes etc. I wondered how much of this is hype and how much is real. So I decided to test it out myself.
First I asked Chat-GPT (in simple spoken language) to write me a neural net code, in particular a Radial Basis Function NN code that can be used in OCTAVE which is essentially a free version of MATLAB. To my wonder, it did write the code that can be used in OCTAVE, using its own training data! That is great. Saves me a lot of time writing and debugging codes.
Next thing I did was to test Chat-GPT’s ability to solve non-linear dynamic differential equation. I first tested it to solve Lorenz attractor, often used in the analysis of chaotic time series. The solutions it gave agreed with those already published !. Next I gave set of non-linear multi-variable set of differential equations which I developed for Chaotic series , in particular for Financial Markets analysis. In solving these Chat-GPT used a number of functions available in OCTAVE (I wasn’t even aware of a lot of them which could be used for my purpose) and gave a solution. I still need to test the prediction But now that I have this code I can test very quickly how well my model works.
Sometime ago, I learnt from a post in Linkdin that that some scientists in Germany have used neural net to solve Schrodinger equation , in some approximate form. May be this will be my next attempt. .
So far all the tests have been on writing codes, getting numerical solutions etc. Since Chat-GPT is AI (neural net) based, next I wanted to try its analytical ability, by asking it to do a simple integral l (which a high school student can do). Boy! Did it fail miserably ! I gave a deep sigh of relief. It was pleasing to know that it cannot do everything. But this relief may not last long. The last I heard was that OpenAI is trying to collaborate with Mathematica to make CHAT-gpt even more general.
It is possible that as more and more knowledge and data is given to AI systems , they can get creative and come up with their own models, may be better model of the interior of earth, and even Universe. Who needs scientists then? Well, for now, I am having fun testing these things.