The frontier in model space is kind of fluid. It's all about solving differential equations.
In theoretical physics, you know the equations, you solve equations analytically, but you can only do that when the model is simple.
In numerical physics, you know the equations, you discretize the problem on a grid, and you solve the constraint defined by the equations with various numerical integration schemes like RK4, but you can only do that when the model is small and you know the equations, and you find a single solution.
Then you want the result faster, so you use mesh-free methods and adaptive grids. It works on bigger models but you have to know the equations, finding a single solution to the differential equations.
Then you compress this adaptive grid with a neural network, while still knowing the governing equations, and you have things like Physics Informed Neural Networks ( https://arxiv.org/pdf/1711.10561 and following papers) where you can bound the approximation error. This method allows solve all solutions to the differential equations simultaneously, sharing the computations.
Then when knowing explicitly your governing equations is too complex, so you assume that there are some governing stochastic equations implicitly, which you learn the end-result of the dynamic with a diffusion model, that's what this alpha-fold is doing.
ML is kind of a memoization technique, analog to hashlife in the game of life, that allows you reuse your past computational efforts. You are free to choose on this ladder which memory-compute trade-off you want to use to model the world.
In theoretical physics, you know the equations, you solve equations analytically, but you can only do that when the model is simple.
In numerical physics, you know the equations, you discretize the problem on a grid, and you solve the constraint defined by the equations with various numerical integration schemes like RK4, but you can only do that when the model is small and you know the equations, and you find a single solution.
Then you want the result faster, so you use mesh-free methods and adaptive grids. It works on bigger models but you have to know the equations, finding a single solution to the differential equations.
Then you compress this adaptive grid with a neural network, while still knowing the governing equations, and you have things like Physics Informed Neural Networks ( https://arxiv.org/pdf/1711.10561 and following papers) where you can bound the approximation error. This method allows solve all solutions to the differential equations simultaneously, sharing the computations.
Then when knowing explicitly your governing equations is too complex, so you assume that there are some governing stochastic equations implicitly, which you learn the end-result of the dynamic with a diffusion model, that's what this alpha-fold is doing.
ML is kind of a memoization technique, analog to hashlife in the game of life, that allows you reuse your past computational efforts. You are free to choose on this ladder which memory-compute trade-off you want to use to model the world.