01. Surrogates

The initial target for developing the Neural Operators is: Physical Simulation Surrogate

• Accuracy
  • L_sim: Simulation for approximating the Physical process
  • L_surrogate: Surrogates for approximating the Simulation
• Scope
  • Sim: one specific physical process
  • Surrogate: the same specific physical process or some specific configs of this physical process

Refer to: https://www.youtube.com/watch?v=lKoJJxjUfdw

Neural Operators introduces a relatively “Flexible Soft Bias” than conventional PDE models.

Partially agree, one direct question is, which kind of params I should add to get this phenomenon? Another type of “inductive bias” on this?

The challenges in Neural Operator is the input x becomes a function…

• Sampling from function space with prob ⇒ Sampling from a proper Random Process

PINN vs NO

Commutative property discussion in Neural Operator