athena__fixed_lno

Module containing implementation of a Laplace Neural Operator layer

This module implements a Laplace Neural Operator (LNO) layer that approximates an integral kernel operator in the Laplace-transform domain. It combines a spectral pathway (encode → spectral mixing → decode) with a local affine bypass:

$\mathbf{v} = \sigma\!\bigl( \underbrace{\mathbf{D}\,\mathbf{R}\,\mathbf{E}\,\mathbf{u}}_{\text{spectral}} + \underbrace{\mathbf{W}\,\mathbf{u}}_{\text{local}} + \mathbf{b}\bigr)$

where: - $\mathbf{u} \in \mathbb{R}^{n_{in}}$ is the discretised input - $\mathbf{E} \in \mathbb{R}^{M \times n_{in}}$ is the Laplace encoder basis: $E_{k,j}=\exp(-s_k\,t_j)$ , $s_k = k\pi$ , $t_j = (j{-}1)/(n_{in}{-}1)$ - $\mathbf{R} \in \mathbb{R}^{M \times M}$ are learnable spectral mixing weights - $\mathbf{D} \in \mathbb{R}^{n_{out} \times M}$ is the Laplace decoder basis: $D_{i,k}=\exp(-s_k\,\tau_i)$ , $\tau_i = (i{-}1)/(n_{out}{-}1)$ - $\mathbf{W} \in \mathbb{R}^{n_{out} \times n_{in}}$ are the local (bypass) weights - $\mathbf{b} \in \mathbb{R}^{n_{out}}$ is the bias - $\sigma$ is the activation function - $M$ = num_modes, the number of Laplace spectral modes

Number of parameters (learnable): $M^2 + n_{out}\,n_{in}$ without bias, $M^2 + n_{out}\,n_{in} + n_{out}$ with bias.

Uses

- athena__onnx_nop_utils
- diffstruc
- athena__misc_types
- coreutils
- athena__base_layer

Interfaces

public interface fixed_lno_layer_type

private module function layer_setup(num_outputs, num_modes, num_inputs, use_bias, activation, kernel_initialiser, bias_initialiser, verbose) result(layer)

Arguments

Type	Intent	Optional		Name
integer,	intent(in)		::	num_outputs
integer,	intent(in)		::	num_modes
integer,	intent(in),	optional	::	num_inputs
logical,	intent(in),	optional	::	use_bias
class(*),	intent(in),	optional	::	activation
class(*),	intent(in),	optional	::	kernel_initialiser
class(*),	intent(in),	optional	::	bias_initialiser
integer,	intent(in),	optional	::	verbose

Return Value type(fixed_lno_layer_type)

Derived Types

type, public, extends(learnable_layer_type) :: fixed_lno_layer_type

Type for a fixed-basis Laplace Neural Operator layer

Components

Type	Visibility	Attributes		Name		Initial
class(base_actv_type),	public,	allocatable	::	activation			Activation function
class(base_init_type),	public,	allocatable	::	bias_init			Initialisers for kernel and bias
character(len=14),	public		::	bias_initialiser	=	''	Initialisers for kernel and bias
integer,	public,	allocatable, dimension(:)	::	bias_shape			Shape of biases
type(array_type),	public		::	decoder_basis			Fixed Laplace decoder basis D [num_outputs x num_modes]
type(array_type),	public		::	encoder_basis			Fixed Laplace encoder basis E [num_modes x num_inputs]
type(graph_type),	public,	allocatable, dimension(:)	::	graph			Graph structure of input data
integer,	public		::	id			Unique identifier
logical,	public		::	inference	=	.false.	Inference mode
integer,	public		::	input_rank	=	0	Rank of input data
integer,	public,	allocatable, dimension(:)	::	input_shape			Input shape
class(base_init_type),	public,	allocatable	::	kernel_init			Initialisers for kernel and bias
character(len=14),	public		::	kernel_initialiser	=	''	Initialisers for kernel and bias
character(len=:),	public,	allocatable	::	name			Layer name
integer,	public		::	num_inputs			Number of inputs (discretisation points)
integer,	public		::	num_modes			Number of Laplace spectral modes
integer,	public		::	num_outputs			Number of outputs (discretisation points)
integer,	public		::	num_params	=	0	Number of learnable parameters
class(array_type),	public,	allocatable, dimension(:,:)	::	output			Output
integer,	public		::	output_rank	=	0	Rank of output data
integer,	public,	allocatable, dimension(:)	::	output_shape			Output shape
type(array_type),	public,	allocatable, dimension(:)	::	params			Learnable parameters
character(len=20),	public		::	subtype	=	repeat(" ", 20)
character(len=4),	public		::	type	=	'base'	Layer type
logical,	public		::	use_bias	=	.false.	Layer has bias
logical,	public		::	use_graph_input	=	.false.	Use graph input
logical,	public		::	use_graph_output	=	.false.	Use graph output
integer,	public,	allocatable, dimension(:,:)	::	weight_shape			Shape of weights
type(array_type),	public,	dimension(1)	::	z			Temporary array for pre-activation values

Constructor

private module function layer_setup (num_outputs, num_modes, num_inputs, use_bias, activation, kernel_initialiser, bias_initialiser, verbose)

Finalizations Procedures

final :: finalise_fixed_lno

Type-Bound Procedures

procedure, public :: add_t_t => add_learnable	Add two layers
procedure, public, pass(this) :: build_from_onnx => build_from_onnx_base	Build layer from ONNX node and initialiser
procedure, public, pass(this) :: emit_onnx_graph_inputs => emit_onnx_graph_inputs_base	Emit graph input tensor declarations for this layer
procedure, public, pass(this) :: emit_onnx_nodes => emit_onnx_nodes_fixed_lno
procedure, public, pass(this) :: extract_output => extract_output_base	Extract the output of the layer as a standard real array
procedure, public, pass(this) :: forward => forward_fixed_lno
procedure, public, pass(this) :: forward_eval => forward_eval_base	Forward pass of layer and return output for evaluation
procedure, public, pass(this) :: get_attributes => get_attributes_fixed_lno
procedure, public, pass(this) :: get_gradients	Get parameter gradients of layer
procedure, public, pass(this) :: get_num_params => get_num_params_fixed_lno
procedure, public, pass(this) :: get_params	Get learnable parameters of layer
procedure, public, pass(this) :: init => init_fixed_lno
procedure, public, pass(this) :: nullify_graph => nullify_graph_base	Nullify the forward pass data of the layer to free memory Read more…
generic, public :: operator(+) => add_t_t	Operator overloading for addition
procedure, public, pass(this) :: print => print_base	Print the layer to a file with additional information
procedure, public, pass(this) :: print_to_unit => print_to_unit_fixed_lno
procedure, public, pass(this) :: read => read_fixed_lno
procedure, public, pass(this) :: reduce => reduce_learnable	Merge another learnable layer into this one
procedure, public, pass(this) :: set_gradients	Set learnable parameters of layer
procedure, public, pass(this) :: set_graph => set_graph_base	Set the graph structure of the input data !! this is adjacency and edge weighting
procedure, public, pass(this) :: set_hyperparams => set_hyperparams_fixed_lno
procedure, public, pass(this) :: set_params	Set learnable parameters of layer
procedure, public, pass(this) :: set_rank => set_rank_base	Set the input and output ranks of the layer
procedure, public, pass(this) :: set_shape => set_shape_base	Set the input shape of the layer

Functions

public function read_fixed_lno_layer(unit, verbose) result(layer)

Read a fixed LNO layer from file and return it

Arguments

Type	Intent	Optional	Attributes		Name
integer,	intent(in)			::	unit	Input unit number
integer,	intent(in),	optional		::	verbose	Verbosity level

Return Value class(base_layer_type), allocatable

Allocated base-layer instance containing the result

private function get_attributes_fixed_lno(this) result(attributes)

Return list of fixed LNO attributes for ONNX export

Arguments

Type	Intent	Optional	Attributes		Name
class(fixed_lno_layer_type),	intent(in)			::	this	Instance of the fixed LNO layer

Return Value type(onnx_attribute_type), allocatable, dimension(:)

List of attributes for ONNX export

private pure function get_num_params_fixed_lno(this) result(num_params)

Return the number of learnable parameters for the layer

Arguments

Type	Intent	Optional	Attributes		Name
class(fixed_lno_layer_type),	intent(in)			::	this	Layer instance

Return Value integer

Total number of learnable parameters

private module function layer_setup(num_outputs, num_modes, num_inputs, use_bias, activation, kernel_initialiser, bias_initialiser, verbose) result(layer)

Arguments

Type	Intent	Optional		Name
integer,	intent(in)		::	num_outputs	Number of output features
integer,	intent(in)		::	num_modes	Number of Laplace spectral modes
integer,	intent(in),	optional	::	num_inputs	Number of input features when known at construction time
logical,	intent(in),	optional	::	use_bias	Whether to allocate a bias term
class(*),	intent(in),	optional	::	activation	Activation function specification
class(*),	intent(in),	optional	::	kernel_initialiser	Kernel and bias initialiser specifications
class(*),	intent(in),	optional	::	bias_initialiser	Kernel and bias initialiser specifications
integer,	intent(in),	optional	::	verbose	Verbosity level

Return Value type(fixed_lno_layer_type)

Constructed fixed LNO layer

Subroutines

private subroutine emit_onnx_nodes_fixed_lno(this, prefix, nodes, num_nodes, max_nodes, inits, num_inits, max_inits, input_name, is_last_layer, format)

Emit decomposed standard ONNX nodes for a Fixed LNO layer.

Arguments

Type	Intent	Optional	Attributes		Name
class(fixed_lno_layer_type),	intent(in)			::	this	Fixed LNO layer instance
character(len=*),	intent(in)			::	prefix	Layer name prefix (e.g. "layer1")
type(onnx_node_type),	intent(inout),		dimension(:)	::	nodes	Node accumulator
integer,	intent(inout)			::	num_nodes	Node counter
integer,	intent(in)			::	max_nodes	Node limit
type(onnx_initialiser_type),	intent(inout),		dimension(:)	::	inits	Initialiser accumulator
integer,	intent(inout)			::	num_inits	Initialiser counter
integer,	intent(in)			::	max_inits	Initialiser limit
character(len=*),	intent(in),	optional		::	input_name	Name of the input tensor
logical,	intent(in),	optional		::	is_last_layer	Whether this is the last layer
integer,	intent(in),	optional		::	format	Export format selector

private subroutine finalise_fixed_lno(this)

Finalise the fixed-basis Laplace neural operator layer

Arguments

Type	Intent	Optional	Attributes		Name
type(fixed_lno_layer_type),	intent(inout)			::	this	Layer instance to release

private subroutine forward_fixed_lno(this, input)

Forward propagation for the Laplace Neural Operator layer

Arguments

Type	Intent	Optional	Attributes		Name
class(fixed_lno_layer_type),	intent(inout)			::	this	Layer instance to execute
class(array_type),	intent(in),		dimension(:,:)	::	input	Input batch tensor collection

private subroutine init_fixed_lno(this, input_shape, verbose)

Initialise parameter storage, fixed bases and output buffers

Arguments

Type	Intent	Optional	Attributes		Name
class(fixed_lno_layer_type),	intent(inout)			::	this	Layer instance to initialise
integer,	intent(in),		dimension(:)	::	input_shape	Input shape used to infer num_inputs
integer,	intent(in),	optional		::	verbose	Verbosity level

private subroutine print_to_unit_fixed_lno(this, unit)

Print fixed LNO settings and parameters to a unit

Arguments

Type	Intent	Optional	Attributes		Name
class(fixed_lno_layer_type),	intent(in)			::	this	Layer instance to print
integer,	intent(in)			::	unit	Output unit number

private subroutine read_fixed_lno(this, unit, verbose)

Arguments

Type	Intent	Optional		Name
class(fixed_lno_layer_type),	intent(inout)		::	this	Layer instance to populate from file data
integer,	intent(in)		::	unit	Input unit number
integer,	intent(in),	optional	::	verbose	Verbosity level

private subroutine set_hyperparams_fixed_lno(this, num_outputs, num_modes, use_bias, activation, kernel_initialiser, bias_initialiser, verbose)

Arguments

Type	Intent	Optional	Attributes		Name
class(fixed_lno_layer_type),	intent(inout)			::	this	Layer instance to configure
integer,	intent(in)			::	num_outputs	Number of output features
integer,	intent(in)			::	num_modes	Number of Laplace spectral modes
logical,	intent(in)			::	use_bias	Whether to use a bias term
class(base_actv_type),	intent(in),		allocatable	::	activation	Activation function object
class(base_init_type),	intent(in),		allocatable	::	kernel_initialiser	Kernel and bias initialiser objects
class(base_init_type),	intent(in),		allocatable	::	bias_initialiser	Kernel and bias initialiser objects
integer,	intent(in),	optional		::	verbose	Verbosity level

athena__fixed_lno_layer Module

Contents

Interfaces

Derived Types

Functions

Subroutines

Uses

Interfaces

public interface fixed_lno_layer_type

private module function layer_setup(num_outputs, num_modes, num_inputs, use_bias, activation, kernel_initialiser, bias_initialiser, verbose) result(layer) Implementation →

Arguments

Return Value type(fixed_lno_layer_type)

Derived Types

type, public, extends(learnable_layer_type) :: fixed_lno_layer_type

Components

Constructor

Finalizations Procedures

Type-Bound Procedures

Functions

public function read_fixed_lno_layer(unit, verbose) result(layer)

Arguments

Return Value class(base_layer_type), allocatable

private function get_attributes_fixed_lno(this) result(attributes)

Arguments

Return Value type(onnx_attribute_type), allocatable, dimension(:)

private pure function get_num_params_fixed_lno(this) result(num_params)

Arguments

Return Value integer

private module function layer_setup(num_outputs, num_modes, num_inputs, use_bias, activation, kernel_initialiser, bias_initialiser, verbose) result(layer)

Arguments

Return Value type(fixed_lno_layer_type)

Subroutines

private subroutine emit_onnx_nodes_fixed_lno(this, prefix, nodes, num_nodes, max_nodes, inits, num_inits, max_inits, input_name, is_last_layer, format)

Arguments

private subroutine finalise_fixed_lno(this)

Arguments

private subroutine forward_fixed_lno(this, input)

Arguments

private subroutine init_fixed_lno(this, input_shape, verbose)

Arguments

private subroutine print_to_unit_fixed_lno(this, unit)

Arguments

private subroutine read_fixed_lno(this, unit, verbose)

Arguments

private subroutine set_hyperparams_fixed_lno(this, num_outputs, num_modes, use_bias, activation, kernel_initialiser, bias_initialiser, verbose)

Arguments

private module function layer_setup(num_outputs, num_modes, num_inputs, use_bias, activation, kernel_initialiser, bias_initialiser, verbose) result(layer)