Polynomial Scaling is Possible For Neural Operator Approximations of Structured Families of BSDEs

arXiv:2410.14788 · math.OC, cs.LG, cs.NA, math.NA, math.PR, q-fin.CP · Submitted 2024-10-18 · Read on arXiv

math.OC, cs.LG, cs.NA, math.NA, math.PR, q-fin.CP

Submitted: 2024-10-18

Updated: 2026-09-22

Comments: 47 pages + references

License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/

Terminology

• Activation Function — 8× in this paper · explained in 1 episode
• Accuracy — 5× in this paper · explained in 1 episode
• DeepONet — 3× in this paper · explained in 2 episodes
• Forward-Backwards Neural Operator — 3× in this paper
• Generalization — 3× in this paper · explained in 13 episodes
• Reinforcement Learning — 3× in this paper · explained in 4 episodes
• Core — 2× in this paper · explained in 2 episodes
• Curse of Dimensionality — 2× in this paper · explained in 6 episodes
• Inverse Problem — 2× in this paper · explained in 2 episodes
• Q-learning — 2× in this paper · explained in 3 episodes
• Scaling Laws — 2× in this paper · explained in 4 episodes
• Actor — 1× in this paper · explained in 3 episodes
• Actor-Critic Learning — 1× in this paper · explained in 1 episode
• American Option Pricing — 1× in this paper · explained in 1 episode
• Approximation Bound — 1× in this paper · explained in 1 episode
• Consistency — 1× in this paper · explained in 3 episodes
• Diffusion Processes — 1× in this paper · explained in 2 episodes
• Higher-order derivatives — 1× in this paper · explained in 2 episodes
• Hilbert Space — 1× in this paper · explained in 2 episodes
• Mixture of Experts — 1× in this paper · explained in 2 episodes
• Non-Markovianity — 1× in this paper · explained in 3 episodes
• Theoretical Guarantees — 1× in this paper · explained in 2 episodes
• Trace — 1× in this paper · explained in 2 episodes
• Transformer — 1× in this paper · explained in 2 episodes
• Verification — 1× in this paper · explained in 2 episodes

Sources

• Do we really need the Rademacher complexities?
• Expansion of Green's function and regularity of Robin's function for elliptic operators in divergence form
• Let data talk: data-regularized operator learning theory for inverse problems
• Global universal approximation of functional input maps on weighted spaces
• Simultaneously Solving Infinitely Many LQ Mean Field Games In Hilbert Spaces: The Power of Neural Operators
• Universal approximation theorem for neural networks with inputs from a topological vector space
• Mixtures of Neural Operators Reduce Active Complexity in Operator Learning
• Generative Neural Operators of Log-Complexity Can Simultaneously Solve Infinitely Many Convex Programs
• Operator Learning of Lipschitz Operators: An Information-Theoretic Perspective
• Nonlocality and Nonlinearity Implies Universality in Operator Learning
• Fourier Neural Operator for Parametric Partial Differential Equations
• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Rough paths, Signatures and the modelling of functions on streams

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