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import jax
from jax import numpy as jnp, random as jr
import equinox as eqx
from typing import List, Callable
from utils import create_lifted_module as clm
class KNO_REG_GRID_1D(eqx.Module):
integration_kernels: List[eqx.Module]
proj_layers: List[eqx.Module]
pointwise_layers: List[eqx.Module]
lift_kernel: eqx.Module
lift_dim: int
depth: int
activation: Callable
def __init__(self, integration_kernel, lift_dim, depth, in_feats, *, key):
keys = jr.split(key,2)
self.integration_kernels = [clm(integration_kernel, lift_dim=lift_dim, key=k) for k in jr.split(keys[0], depth)]
self.pointwise_layers = [eqx.nn.Conv(1, lift_dim, lift_dim, 1, key=key) for key in jr.split(keys[1], depth)]
keys = jr.split(keys[0],4)
self.proj_layers = [eqx.nn.Linear(lift_dim, lift_dim, key=keys[0]),
eqx.nn.Linear(lift_dim, lift_dim, key=keys[1]),
eqx.nn.Linear(lift_dim, 1, key=keys[2])]
self.lift_kernel = eqx.nn.Linear(in_feats, lift_dim, key=keys[3])
self.activation = jax.nn.gelu
self.lift_dim = lift_dim
self.depth = depth
def __call__(self,
f_x, ### input fn, note no batch dim
x_grid,
q_weights,
):
def integration_transform(int_kernel,
q_nodes, ### quad nodes
q_weights, ### quad weights
f_q):
G = (int_kernel(q_nodes,q_nodes)) * q_weights.T
f_q = jnp.einsum('q,kq->k',f_q, G)
return f_q
q_nodes = x_grid
f_q = f_x ### already at quad nodes
f_q = jnp.concatenate((f_q,q_nodes), axis=-1)
f_q = eqx.filter_vmap(self.lift_kernel)(f_q)
f_q = self.activation(f_q)
for i in range(self.depth-1):
f_q_skip = self.pointwise_layers[i](f_q.T).T
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),1), out_axes=1)(self.integration_kernels[i],
f_q)
f_q = f_q_skip + f_q
f_q = self.activation(f_q)
f_q_skip = self.pointwise_layers[-1](f_q.T).T
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),1), out_axes=1)(self.integration_kernels[-1],
f_q)
f_q = f_q_skip + f_q
f_q = self.activation(eqx.filter_vmap(self.proj_layers[0])(f_q))
f_q = self.activation(eqx.filter_vmap(self.proj_layers[1])(f_q))
f_q = eqx.filter_vmap(self.proj_layers[2])(f_q)
f_q = f_q.squeeze()
return f_q
### 3d non-factorized model with interpolant on the backend
class KNO_DIFFUSION_REACTION(eqx.Module):
output_kernel: eqx.Module
integration_kernels: List[eqx.Module]
proj_layers: List[eqx.Module]
pointwise_layers: List[eqx.Module]
lift_kernel: eqx.Module
lift_dim: int
depth: int
activation: Callable
def __init__(self, output_kernel, integration_kernel, lift_dim, depth, in_feats, *, key):
keys = jr.split(key)
self.integration_kernels = [clm(integration_kernel, lift_dim=lift_dim, key=k) for k in jr.split(keys[0], depth)]
self.pointwise_layers = [eqx.nn.Conv(1, lift_dim, lift_dim, 1, key=key) for key in jr.split(keys[1], depth)]
keys = jr.split(keys[0],4)
self.proj_layers = [eqx.nn.Linear(lift_dim, lift_dim, key=keys[0]),
eqx.nn.Linear(lift_dim, lift_dim, key=keys[1]),
eqx.nn.Linear(lift_dim, 1, key=keys[2])]
self.lift_kernel = eqx.nn.Linear(in_feats, lift_dim, key=keys[3])
keys = jr.split(keys[0])
self.output_kernel = output_kernel(key=keys[0])
self.activation = jax.nn.gelu
self.lift_dim = lift_dim
self.depth = depth
def __call__(self,
f_x, ### input fn, note no batch dim
y_grid,
q_nodes,
q_weights,
):
def integration_transform(int_kernel,
q_nodes, ### quad nodes
q_weights, ### quad weights
f_q):
G = (int_kernel(q_nodes,q_nodes)) * q_weights.T
f_q = jnp.einsum('q,kq->k',f_q, G)
return f_q
f_x = jnp.concatenate((f_x,q_nodes), axis=-1)
f_q = eqx.filter_vmap(self.lift_kernel)(f_x)
f_q = self.activation(f_q)
for i in range(self.depth-1):
f_q_skip = self.pointwise_layers[i](f_q.T).T
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),1),
out_axes=1)(self.integration_kernels[i],
f_q)
f_q = f_q_skip + f_q
f_q = self.activation(f_q)
f_q_skip = self.pointwise_layers[-1](f_q.T).T
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),1),
out_axes=1)(self.integration_kernels[-1],
f_q)
f_q = f_q_skip + f_q
f_q = self.activation(eqx.filter_vmap(self.proj_layers[0])(f_q))
f_q = self.activation(eqx.filter_vmap(self.proj_layers[1])(f_q))
f_q = eqx.filter_vmap(self.proj_layers[2])(f_q)
f_q = f_q.reshape(len(q_nodes),1)
### move to grid
Kqq = self.output_kernel(q_nodes,q_nodes) + (jnp.eye(len(q_nodes)) * 1e-5)
Kqy = self.output_kernel(q_nodes, y_grid)
KyqKqqInv = jnp.linalg.solve(Kqq, Kqy).T
f_y = jnp.einsum('mc,qm->qc', f_q, KyqKqqInv)
return f_y
### 2d factorized model for regular grid
class KNO_DARCY_PWC(eqx.Module):
integration_kernels: List[eqx.Module]
lift_kernel: eqx.Module
depth: int
proj_layers: eqx.Module
pointwise_layers: List[eqx.Module]
d: int
lift_dim: int
in_feats: int
def __init__(self,
integration_kernel,
depth,
lift_dim,
ndims,
in_feats,
key,
):
keys = jr.split(key, 7)
self.lift_dim = lift_dim
self.d = ndims
self.proj_layers = [eqx.nn.Linear(lift_dim, lift_dim, key=keys[0]),
eqx.nn.Linear(lift_dim, lift_dim, key=keys[1]),
eqx.nn.Linear(lift_dim, 1, key=keys[2])]
self.pointwise_layers = [eqx.nn.Conv(1, lift_dim, lift_dim, 1, key=key) for key in jr.split(keys[3], depth)]
self.lift_kernel = eqx.nn.Linear(in_feats,lift_dim,key=keys[4])
self.integration_kernels = [(clm(integration_kernel, lift_dim, k1),
clm(integration_kernel, lift_dim, k2)) for k in jr.split(keys[5],depth) for k1,k2 in [jr.split(k, ndims)]]
self.in_feats = in_feats
self.depth = depth
def __call__(self,
f_x, ### input fn, note no batch dim
x_grid,
q_weights,
):
def integration_transform(int_kernel,
q, ### quad nodes
w, ### quad weights
f_q):
G1 = int_kernel[0](q,q) * w.T
G2 = int_kernel[1](q,q) * w.T
f_q = jnp.einsum('ij,ki->kj',f_q, G1) + jnp.einsum('ij,kj->ik',f_q, G2)
return f_q
q_nodes = x_grid[:,0,0] ## grab 1d x grid
f_x = jnp.concatenate((f_x,x_grid), axis=-1)
f_x = f_x.reshape(-1,self.in_feats)
f_x = eqx.filter_vmap(self.lift_kernel)(f_x)
f_x = f_x.reshape(len(q_nodes), len(q_nodes), self.lift_dim)
f_q = f_x
for i in range(self.depth-1):
f_q_skip = self.pointwise_layers[i](f_q.reshape(-1,self.lift_dim).T).T
f_q_skip = f_q_skip.reshape(f_q.shape)
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),self.d),
out_axes=self.d)(self.integration_kernels[i],
f_q)
f_q = f_q_skip + f_q
f_q = jax.nn.gelu(f_q)
f_q_skip = self.pointwise_layers[-1](f_q.reshape(-1,self.lift_dim).T).T
f_q_skip = f_q_skip.reshape(f_q.shape)
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),self.d),
out_axes=self.d)(self.integration_kernels[-1],
f_q)
f_q = f_q + f_q_skip
f_q = f_q.reshape(-1,self.lift_dim)
f_q = jax.nn.gelu(eqx.filter_vmap(self.proj_layers[0])(f_q))
f_q = jax.nn.gelu(eqx.filter_vmap(self.proj_layers[1])(f_q))
f_q = eqx.filter_vmap(self.proj_layers[2])(f_q)
f_y = f_q
return f_y
### 2D non-factorized model with trainable interpolant on both ends
class KNO_DARCY_TRIANGLE(eqx.Module):
input_kernel: eqx.Module
output_kernel: eqx.Module
integration_kernels: List[eqx.Module]
proj_layers: List[eqx.Module]
pointwise_layers: List[eqx.Module]
lift_kernel: eqx.Module
lift_dim: int
depth: int
activation: Callable
def __init__(self, input_kernel, output_kernel, integration_kernel, lift_dim, depth, in_feats, *, key):
keys = jr.split(key,2)
self.integration_kernels = [clm(integration_kernel, lift_dim=lift_dim, key=k) for k in jr.split(keys[0], depth)]
self.pointwise_layers = [eqx.nn.Conv(1, lift_dim, lift_dim, 1, key=key) for key in jr.split(keys[1], depth)]
keys = jr.split(keys[0],4)
self.proj_layers = [eqx.nn.Linear(lift_dim, lift_dim, key=keys[0]),
eqx.nn.Linear(lift_dim, lift_dim, key=keys[1]),
eqx.nn.Linear(lift_dim, 1, key=keys[2])]
self.lift_kernel = eqx.nn.Linear(in_feats, lift_dim, key=keys[3])
keys = jr.split(keys[0], 2)
self.input_kernel = input_kernel(key=keys[0])
self.output_kernel = output_kernel(key=keys[1])
self.activation = jax.nn.gelu
self.lift_dim = lift_dim
self.depth = depth
def __call__(self,
f_x, ### input fn, note no batch dim
x_grid,
y_grid,
q_nodes,
q_weights,
):
def integration_transform(int_kernel,
q_nodes, ### quad nodes
q_weights, ### quad weights
f_q):
G = (int_kernel(q_nodes,q_nodes)) * q_weights.T
f_q = jnp.einsum('q,kq->k',f_q, G)
return f_q
f_x = jnp.concatenate((f_x,x_grid), axis=-1)
f_x = eqx.filter_vmap(self.lift_kernel)(f_x)
f_x = f_x.reshape(len(x_grid),self.lift_dim)
Kxx = self.input_kernel(x_grid, x_grid) + (jnp.eye(len(x_grid)) * 1e-5)
Kxq = self.input_kernel(x_grid, q_nodes)
KqxKinv = jnp.linalg.solve(Kxx, Kxq).T
f_q = jnp.einsum('mc,qm->qc', f_x, KqxKinv)
f_q = self.activation(f_q)
for i in range(self.depth-1):
f_q_skip = self.pointwise_layers[i](f_q.T).T
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),1), out_axes=1)(self.integration_kernels[i],
f_q)
f_q = f_q_skip + f_q
f_q = self.activation(f_q)
f_q_skip = self.pointwise_layers[-1](f_q.T).T
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),1), out_axes=1)(self.integration_kernels[-1],
f_q)
f_q = f_q_skip + f_q
f_q = self.activation(eqx.filter_vmap(self.proj_layers[0])(f_q))
f_q = self.activation(eqx.filter_vmap(self.proj_layers[1])(f_q))
f_q = eqx.filter_vmap(self.proj_layers[2])(f_q)
Iqq = jnp.eye(len(q_nodes)) * 1e-5
Kqq = self.output_kernel(q_nodes,q_nodes) + Iqq
Kqy = self.output_kernel(q_nodes, y_grid)
KyqKqqInv = jnp.linalg.solve(Kqq, Kqy).T
f_y = jnp.einsum('mc,qm->qc', f_q, KyqKqqInv)
return f_y
### 2D factorized model where each dim has a slightly different quad rule
class KNO_NS_PIPE(eqx.Module):
integration_kernels: List[eqx.Module]
lift_kernel: eqx.Module
depth: int
proj_layers: eqx.Module
pointwise_layers: List[eqx.Module]
d: int
lift_dim: int
res_1d: int
activation: Callable
def __init__(self,
integration_kernel,
depth,
lift_dim,
ndims,
in_feats,
res_1d,
key,
):
keys = jr.split(key, 7)
self.lift_dim = lift_dim
self.d = ndims
self.proj_layers = [eqx.nn.Linear(lift_dim, lift_dim, key=keys[0]),
eqx.nn.Linear(lift_dim, lift_dim, key=keys[1]),
eqx.nn.Linear(lift_dim, 1, key=keys[2])]
self.pointwise_layers = [eqx.nn.Conv(1, lift_dim, lift_dim, 1, key=key) for key in jr.split(keys[3], depth)]
self.lift_kernel = eqx.nn.Linear(in_feats,lift_dim,key=keys[4])
self.integration_kernels = [(clm(integration_kernel, lift_dim, k1), clm(integration_kernel, lift_dim, k2)) for k in jr.split(keys[5],depth) for k1,k2 in [jr.split(k, ndims)]]
self.depth = depth
self.res_1d = res_1d
self.activation = jax.nn.gelu
def __call__(self,q,wx,wy):
grid_1d_y = q[0, :, 1]
grid_1d_x = q[:, 0, 0]
def integration_transform(int_kernel,
f_q):
G1 = int_kernel[0](grid_1d_x,grid_1d_x) * wx.T
G2 = int_kernel[1](grid_1d_y,grid_1d_y) * wy.T
f_q = jnp.einsum('ij,ki->kj',f_q, G1) + jnp.einsum('ij,kj->ik',f_q, G2)
return f_q
q = q.reshape(-1,2)
f_x = eqx.filter_vmap(self.lift_kernel)(q)
f_x = f_x.reshape(self.res_1d,self.res_1d,self.lift_dim)
f_q = f_x
for i in range(self.depth-1):
f_q_skip = self.pointwise_layers[i](f_q.reshape(-1,self.lift_dim).T).T
f_q_skip = f_q_skip.reshape(f_q.shape)
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,f), in_axes=(eqx.if_array(0),self.d), out_axes=self.d)(self.integration_kernels[i],
f_q)
f_q = f_q_skip + f_q
f_q = self.activation(f_q)
f_q_skip = self.pointwise_layers[-1](f_q.reshape(-1,self.lift_dim).T).T
f_q_skip = f_q_skip.reshape(f_q.shape)
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,f), in_axes=(eqx.if_array(0),self.d), out_axes=self.d)(self.integration_kernels[i+1],f_q)
f_q = f_q + f_q_skip
f_q = f_q.reshape(-1,self.lift_dim)
f_q = self.activation(eqx.filter_vmap(self.proj_layers[0])(f_q))
f_q = self.activation(eqx.filter_vmap(self.proj_layers[1])(f_q))
f_y = eqx.filter_vmap(self.proj_layers[2])(f_q)
return f_y
### 3D factorized model
class KNO_NS_3D(eqx.Module):
integration_kernels: List[eqx.Module]
lift_kernel: eqx.Module
depth: int
proj_layers: eqx.Module
pointwise_layers: List[eqx.Module]
d: int
lift_dim: int
in_feats: int
res_1d: int
activation: Callable
def __init__(self,
integration_kernel,
depth,
lift_dim,
ndims,
in_feats,
res_1d,
key,
):
keys = jr.split(key, 7)
self.lift_dim = lift_dim
self.d = ndims
self.proj_layers = [eqx.nn.Linear(lift_dim, lift_dim, key=keys[0]),
eqx.nn.Linear(lift_dim, lift_dim, key=keys[1]),
eqx.nn.Linear(lift_dim, 1, key=keys[2])]
self.pointwise_layers = [eqx.nn.Conv(1, lift_dim, lift_dim, 1, key=key) for key in jr.split(keys[3], depth)]
self.lift_kernel = eqx.nn.Linear(in_feats,lift_dim,key=keys[4])
self.integration_kernels = [(clm(integration_kernel, lift_dim, k1), clm(integration_kernel, lift_dim, k2),
clm(integration_kernel, lift_dim, k3)) for k in jr.split(keys[5],depth) for k1,k2,k3 in [jr.split(k, ndims)]]
self.in_feats = in_feats
self.depth = depth
self.res_1d = res_1d
self.activation = jax.nn.gelu
def __call__(self,
f_x, ### input fn, note no batch dim
x_grid,
q_weights,
):
def integration_transform(int_kernel,
q, ### quad nodes
w, ### quad weights
f_q):
G1 = int_kernel[0](q,q) * w.T
G2 = int_kernel[1](q,q) * w.T
G3 = int_kernel[2](q,q) * w.T
f_q = jnp.einsum('ijk,li->ljk', f_q, G1) \
+ jnp.einsum('ijk,lj->ilk', f_q, G2) \
+ jnp.einsum('ijk,lk->ijl', f_q, G3)
return f_q
q_nodes = x_grid[:,0,0,1]
f_x = jnp.concatenate((f_x,x_grid), axis=-1)
f_x = f_x.reshape(-1,self.in_feats)
f_x = eqx.filter_vmap(self.lift_kernel)(f_x)
f_q = f_x.reshape(len(q_nodes), len(q_nodes), len(q_nodes), self.lift_dim)
for i in range(self.depth-1):
f_q_skip = self.pointwise_layers[i](f_q.reshape(-1,self.lift_dim).T).T
f_q_skip = f_q_skip.reshape(f_q.shape)
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),self.d), out_axes=self.d)(self.integration_kernels[i],
f_q)
f_q = f_q_skip + f_q
f_q = self.activation(f_q)
f_q_skip = self.pointwise_layers[-1](f_q.reshape(-1,self.lift_dim).T).T
f_q_skip = f_q_skip.reshape(f_q.shape)
f_q = eqx.filter_vmap(lambda int_kernel, f: integration_transform(int_kernel,q_nodes,q_weights,f),
in_axes=(eqx.if_array(0),self.d), out_axes=self.d)(self.integration_kernels[-1],
f_q)
f_q = f_q + f_q_skip
f_q = f_q.reshape(-1,self.lift_dim)
f_q = self.activation(eqx.filter_vmap(self.proj_layers[0])(f_q))
f_q = self.activation(eqx.filter_vmap(self.proj_layers[1])(f_q))
f_y = eqx.filter_vmap(self.proj_layers[2])(f_q)
return f_y