15 problems

Conjecture that the uniform state-space regularity assumption can be avoided
arXiv@arxiv
The framework considers neural operators with activation base functions $(\sigma_i)_{1\leq i\leq L}$ and a uniform state-space regularity assumption expressed by … can be avoided.…
Conjectureopenneural-operators operator-learning partial-differential-equations
1
Conjecture that weaker kernel singularities yield faster convergence
arXiv@arxiv
Weaker-singularity convergence conjecture. Kernels with weaker singularities should converge more rapidly.
Conjectureopenkernel-methods neural-operators numerical-analysis
1
Conjecture on operator-dependent parameterization and approximation gaps
arXiv@arxiv
Consider an operator-inverse trick whose parameterization depends on the operator being approximated. Operator-dependent parameterization conjecture. The observed behavior is due t…
Conjectureopenneural-operators operator-learning optimization
0
Conjecture on instability from fast-decaying spectra and minibatch noise
arXiv@arxiv
The OMM is applied to the operator $-\mathpzc{H}$ to retrieve its top eigenvalues and eigenfunctions, where $\mathpzc{H}$ is a Hamiltonian operator and the optimization uses miniba…
Conjectureopeneigenvalue-problems neural-operators optimization
0
Poseidon's prior-knowledge conjecture for fluid-type PDE datasets
arXiv@arxiv
The [? Let Poseidon be a neural operator model pretrained on fluid-type datasets, and consider the INS-Tracer equation dataset, whose physical mechanisms include incompressible Nav…
Conjectureopenmachine-learning neural-operators partial-differential-equations
1
NASM's architectural explanation for ID/OOD generalization
arXiv@arxiv
NASM is a neural adaptive spectral method whose architecture explicitly disentangles coefficients from basis functions. NASM generalization conjecture. We conjecture that NASM's ab…
Conjectureopengeneralization neural-operators spectral-methods
0
Overparameterization Improves Optimization for Neural Operators
arXiv@arxiv
Let a neural operator have adjustable capacity, for example through its number of layers or neurons, and consider the non-convex optimization landscape of its training loss. Overpa…
Conjectureopendeep-learning neural-operators optimization
0
Conjecture that accuracy degradation is linked to high-fidelity solver robustness
arXiv@arxiv
The hybrid simulations use a high-fidelity solver for relaxation time steps, but their initial conditions may be unphysical as a result of the learned model's predictions. Robustne…
Conjectureopenneural-operators numerical-analysis phase-field-modeling
0
Conjecture on over-smoothing by baseline Fourier neural operators
arXiv@arxiv
Consider learning the solution operator for the two-dimensional Navier–Stokes equations at Reynolds number $\operatorname{Re}=5000$ , where turbulent flow produces small-scale featu…
Conjectureopenmachine-learning navier-stokes neural-operators
0
Conjecture on embedding dimension and local-kernel expressivity in neural operators
arXiv@arxiv
The models use local kernels together with an embedding dimension, and numerical experiments indicate that larger embedding dimensions and fewer modes can improve performance while…
Conjectureopenmachine-learning neural-operators numerical-analysis
0
The pure-data-loss explanation for unphysical prediction artifacts
arXiv@arxiv
The authors train neural-network models to predict the velocity and pressure fields of two-dimensional incompressible Navier–Stokes flows from channel-flow data, comparing a pure d…
Conjectureopennavier-stokes neural-operators physics-informed-machine-learning
0
Conjecture on approximation bias from linear superposition in nonlinear problems
arXiv@arxiv
The discussion concerns neural operators that approximate complex nonlinear problems using a linear superposition method. Approximation-bias conjecture. The approximation bias intr…
Conjectureopenapproximation-theory neural-operators
1
DeepONet's inefficiency for translation, rotation, and stretching symmetries
arXiv@arxiv
The DeepONet is a neural operator architecture whose trunk and branch networks form a linear projection-based representation of the target operator. In the toy problem, the dynamic…
Conjectureopendeep-learning neural-operators symmetry
1
Conjecture on problem-specific features compensating for DeepONet biases
arXiv@arxiv
Neural operators, PCA-based operator approximations, and DeepONets use different finite-dimensionalizations of their input and output function spaces. In the basic form of DeepONet…
Conjectureopendeep-learning neural-operators operator-learning
0
Conjecture on the success of diagonal initialization for Burgers equation transformers
arXiv@arxiv
The input consists of initial conditions, and the target consists of solutions at $t=1$ ; these are represented by the blue and green curves, respectively, in Figure. The model uses…
Conjectureopeninitialization neural-operators transformers
0