CUDA FNO1D (real RFFT fused path)

This file provides a CUDA-only forward + VJP wrapper for a small real-valued FNO1D model whose spectral convolution is implemented by the fused cuFFT-backed primitive Tape.spectralConv1dRfft.

Why this is not a TorchLean.NN.LayerDef:

• LayerDef is backend-polymorphic and runs through the Torch.Ops interface.
• The fused spectralConv1dRfft op is implemented only for the CUDA tape backend.

This module is meant to be called by runnable examples that want the performance path, while the portable reference path lives in NN.Runtime.Autograd.TorchLean.Fno1d.

@[reducible, inline]

abbrev Runtime.Autograd.Cuda.Fno1dRfftFused.vec (n : ℕ) : Spec.Shape

Runtime vector shape abbreviation used by the small fused FNO wrapper.

@[reducible, inline]

abbrev Runtime.Autograd.Cuda.Fno1dRfftFused.mat (m n : ℕ) : Spec.Shape

Runtime matrix shape abbreviation used by the small fused FNO wrapper.

structure Runtime.Autograd.Cuda.Fno1dRfftFused.Param : Type

Trainable parameter plus Adam moment buffers.

All three arrays use the same row-major layout for shape. The value array is uploaded to CUDA when building a tape; the moment arrays stay on the host because this small wrapper performs Adam updates in Lean after downloading gradients.

• shape : Spec.Shape

  Runtime tensor shape for value, m, and v.

• value : FloatArray

  Current parameter values in row-major order.

• m : FloatArray

  Adam first-moment accumulator.

• v : FloatArray

  Adam second-moment accumulator.

structure Runtime.Autograd.Cuda.Fno1dRfftFused.Forward : Type

Output of one fused-FNO tape construction.

• tape : Tape

  The completed CUDA tape.

• predId : ℕ

  Node id of the prediction tensor.

• lossId? : Option ℕ

  Optional scalar loss node id, present only when a target was supplied.

• paramIds : Array ℕ

  Tape node ids for parameters, in the same order as the parameter array.

structure Runtime.Autograd.Cuda.Fno1dRfftFused.AdamState : Type

Minimal Adam state carried across fused-FNO training steps.

• step : ℕ

  Step counter (1-based in the Adam bias correction formulas).

• beta1Pow : Float

  Cached beta1^step for bias correction (starts at 1).

• beta2Pow : Float

  Cached beta2^step for bias correction (starts at 1).

def Runtime.Autograd.Cuda.Fno1dRfftFused.zerosArray (n : ℕ) : FloatArray

Allocate a zero-filled FloatArray of length n.

def Runtime.Autograd.Cuda.Fno1dRfftFused.lcgNext (s : ℕ) : ℕ

One step of the small deterministic LCG used for fused-FNO parameter initialization.

This stays local to the fused CUDA example path so the engine layer does not depend on the higher-level Torch.Init helper namespace.

def Runtime.Autograd.Cuda.Fno1dRfftFused.rand01 (seed idx : ℕ) : Float

Deterministic pseudo-random number in [0, 1) derived from seed and a scalar index.

def Runtime.Autograd.Cuda.Fno1dRfftFused.rand01.go : ℕ → ℕ → ℕ

def Runtime.Autograd.Cuda.Fno1dRfftFused.uniformAt (seed idx : ℕ) (lo hi : Float) : Float

Deterministic uniform sample in [lo, hi) for a scalar index.

def Runtime.Autograd.Cuda.Fno1dRfftFused.initFloatArray (shape : Spec.Shape) (seed : ℕ) (lo hi : Float) : FloatArray

Initialize a row-major parameter array with deterministic uniform samples.

def Runtime.Autograd.Cuda.Fno1dRfftFused.initParam (shape : Spec.Shape) (seed : ℕ) (lo hi : Float) : Param

Initialize a trainable parameter and zero Adam moments.

def Runtime.Autograd.Cuda.Fno1dRfftFused.initBias (shape : Spec.Shape) : Param

Initialize a bias-like parameter at zero with zero Adam moments.

def Runtime.Autograd.Cuda.Fno1dRfftFused.initParams (grid width modes blocks seed : ℕ) : Array Param

Initialize parameters for the fused FNO1D model:

• input lift: W_in : (1,width), b_in : (width)
• blocks: (wRe,wIm) : (modes,width,width), wSkip : (width,width), bSkip : (width)
• output proj: W_out : (width,1), b_out : (1)

def Runtime.Autograd.Cuda.Fno1dRfftFused.getParam (ps : Array Param) (i : ℕ) : Result Param

Fetch a parameter with an error message that points to the fused-FNO wrapper.

def Runtime.Autograd.Cuda.Fno1dRfftFused.addParamLeaf (t : Tape) (ps : Array Param) (paramIds : Array ℕ) (i : ℕ) : Result (Tape × Array ℕ × ℕ)

Upload parameter i as a gradient-requiring CUDA tape leaf and record its node id.

def Runtime.Autograd.Cuda.Fno1dRfftFused.broadcastVecToMat (t : Tape) (grid cols xId : ℕ) : Result (Tape × ℕ)

Broadcast a vector of length cols across grid rows.

def Runtime.Autograd.Cuda.Fno1dRfftFused.forward (grid width modes blocks : ℕ) (ps : Array Param) (x : Spec.Tensor Float (vec grid)) (target? : Option (Spec.Tensor Float (vec grid))) : Result Forward

Build a CUDA tape that computes prediction (and optionally MSE loss) for the fused real-RFFT FNO.

Inputs:

• x : (grid) (interpreted as (grid,1)),
• optional target : (grid).

def Runtime.Autograd.Cuda.Fno1dRfftFused.scalarFromTape (t : Tape) (id : ℕ) : Result Float

Download a scalar CUDA tape value to host Float.

def Runtime.Autograd.Cuda.Fno1dRfftFused.predFromTape (grid : ℕ) (t : Tape) (id : ℕ) : Result (Spec.Tensor Float (vec grid))

Download a (grid,1) prediction matrix as a length-grid tensor.

def Runtime.Autograd.Cuda.Fno1dRfftFused.meanLoss (grid width modes blocks : ℕ) (ps : Array Param) (samples : List (Spec.Tensor Float (vec grid) × Spec.Tensor Float (vec grid))) : Result Float

Mean MSE loss over a host-side list of (input,target) samples.

def Runtime.Autograd.Cuda.Fno1dRfftFused.adamUpdateArrayBiasCorrected (value m v grad : FloatArray) (lr beta1 beta2 eps biasCorr1 biasCorr2 : Float) : FloatArray × FloatArray × FloatArray

Host-side Adam update for one flattened parameter array.

Bias correction factors are passed in already computed as 1 - beta₁^t and 1 - beta₂^t.

def Runtime.Autograd.Cuda.Fno1dRfftFused.updateParamsAdam (ps : Array Param) (fw : Forward) (lr : Float) (st : AdamState) (beta1 : Float := 0.9) (beta2 : Float := 0.999) (eps : Float := 1e-8) : Result (Array Param × AdamState)

Run reverse-mode on the fused-FNO tape and update every recorded parameter with Adam.

Gradients are computed on CUDA buffers and downloaded to host arrays before the update. A high-throughput optimizer kernel should live in a separate CUDA optimizer layer, not inside this model helper.