Modulus Sym Configuration

Modulus Sym employs an extension of the Hydra configuration framework to offer a highly customizable but user friendly method for configuring the majority of Modulus Sym’ features. This is achieved by using easy to understand YAML files which contain essential hyperparameters for any physics-informed deep learning model. While you can still achieve the same level of customization in Modulus Sym as any deep learning library, our built in configuration framework allows many of the internal features to be much more accessible. This section provides an overview of the built in configurable API Modulus Sym provides.

Generally speaking, Modulus Sym follows the same work flow as Hydra with just some minor differences. For each Modulus Sym program you should create a YAML configuration file that is then loaded into a Python ModulusConfig object which is used by Modulus Sym. Consider the following example:

Listing 15 conf/config.yaml

            

            
defaults:
 - modulus_default
 - arch:
    - fully_connected
 - optimizer: adam
 - scheduler: exponential_lr
 - loss: sum
        

Listing 16 main.py

            

            
import modulus.sym
from modulus.sym.hydra import to_yaml
from modulus.sym.hydra.config import ModulusConfig

@modulus.main(config_path="conf", config_name="config")
def run(cfg: ModulusConfig) -> None:
    print(to_yaml(cfg))

if __name__ == "__main__":
   run()
        

Here, a minimal configuration (config) YAML file is shown. A defaults list in config.yaml is used to load predefined configurations that are supported by Modulus Sym. This config file is then loaded into python using the @modulus.main() decorator, in which you specify the location and name of your custom config. The config object, cfg, is then ingested into Modulus Sym and used to setup all sorts of internals all of which can be individually customized as discussed in the following sections.

For this example, Modulus Sym has been configured to load a fully connected neural network, ADAM optimizer, exponential decay LR scheduler and a summation loss aggregation. Each of the included examples present in this user guide has its own config file which can be referenced.

Configs in Modulus Sym are required to follow a common structure to ensure that all necessary parameters are provided independent of the user explicitly providing them. This is done by specifying the modulus_default schema at the top of the defaults list in every configuration file which will create the following config structure:

            

            
config
 |
 | <General parameters>
 |
 |- arch
     | <Architecture parameters>
 |- training
     | <Training parameters>
 |- loss
     | <Loss parameters>
 |- optimizer
     | <Optimizer parameters>
 |- scheduler
     | <Scheduler parameters>
 |- profiler
     | <Profiler parameters>
        

This config object has multiple configuration groups that each contain separate parameters pertaining to various features needed inside of Modulus Sym. As seen in the example above, these groups can be quickly populated in the defaults list (e.g. optimizer: adam will populate the optimizer configuration group with parameters needed for ADAM). The next section takes a look at each of these groups in greater detail.

Global Parameters

Some essential parameters that you will find in a Modulus Sym configuration include:

• jit: Turn on TorchScript

• save_filetypes: Types of file outputs from constraints, validators and inferencers

• debug: Turn on debug logging

• initialization_network_dir: Custom location to load pretrained models from

Architecture

The architecture config group holds a list of model configurations that can be used to create different built in neural networks present within Modulus Sym. While not required by the Modulus Sym solver, this parameter group allows you to tune model architectures through the YAML config file or even the command line.

To initialize an architecture using the config, Modulus Sym provides an instantiate_arch() method that allows different architectures to be initialized easily. The following two examples initialize the same neural network.

Listing 17 Config model intialization

            

            
# config/config.yaml
defaults:
    - modulus_default
    - arch:
        - fully_connected

# Python code
import modulus.sym
from modulus.sym.hydra import instantiate_arch
from modulus.sym.hydra.config import ModulusConfig

@modulus.main(config_path="conf", config_name="config")
def run(cfg: ModulusConfig) -> None:
    model = instantiate_arch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("u"), Key("v"), Key("p")],
        cfg=cfg.arch.fully_connected,
    )


if __name__ == "__main__":
    run()
        

Listing 18 Explicit model intialization

            

            
# Python code
import modulus.sym
from modulus.sym.hydra.config import ModulusConfig
from modulus.sym.models.fully_connected import FullyConnectedArch

@modulus.main(config_path="conf", config_name="config")
def run(cfg: ModulusConfig) -> None:
    model = FullyConnectedArch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("u"), Key("v"), Key("p")],
        layer_size: int = 512,
        nr_layers: int = 6,
        ...
    )

if __name__ == "__main__":
    run()
        

Currently the architectures that are shipped internally in Modulus Sym that have a configuration group include:

• fully_connected: Fully connected neural network model

• fourier_net: Fourier neural network

• highway_fourier: Highway Fourier Network - Fourier neural network with adaptive gating units

• modified_fourier: Modified Fourier Network - Fourier neural network with two layers of Fourier features

• multiplicative_fourier: Fourier feature neural network with frequency connections

• multiscale_fourier: Multi-scale Fourier Feature Network - Multi-scale Fourier feature neural network

• siren: Sinusoidal Representation Networks (SiReNs) - Sinusoidal representation networks

• hash_net: Neural network augmented by a multiresolution hash table

• fno: Fourier Neural Operator - 1D, 2D, or 3D Fourier neural operator

• afno: Adaptive Fourier Neural Operator - Fourier neural operator based transformer model

• super_res: Super Resolution Net - Convolutional super resolution model

• pix2pix: Pix2Pix Net - A pix2pix based convolutional encoder-decoder

Examples

Listing 19 Initialization of fully-connected model with 5 layers of size 128

            

            
# config.yaml
defaults:
    - modulus_default
    - arch:
        - fully_connected

arch:
    fully_connected:
        layer_size: 512
        nr_layers: 6


# Python code
import modulus.sym
from modulus.sym.hydra import instantiate_arch
from modulus.sym.hydra.config import ModulusConfig

@modulus.main(config_path="conf", config_name="config")
def run(cfg: ModulusConfig) -> None:
    model = instantiate_arch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("u"), Key("v")],
        cfg=cfg.arch.fully_connected,
    )

if __name__ == "__main__":
    run()
        

Listing 20 Initialization of modified fourier model and siren model

            

            
# config.yaml
defaults:
    - modulus_default
    - arch:
        - modified_fourier
        - siren


# Python code
import modulus.sym
from modulus.sym.hydra import instantiate_arch
from modulus.sym.hydra.config import ModulusConfig

@modulus.main(config_path="conf", config_name="config")
def run(cfg: ModulusConfig) -> None:
    model_1 = instantiate_arch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("u"), Key("v")],
        frequencies=("axis,diagonal", [i / 2.0 for i in range(10)]),
        cfg=cfg.arch.modified_fourier,
    )

    model_2 = instantiate_arch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("u"), Key("v")],
        cfg=cfg.arch.siren,
    )


if __name__ == "__main__":
    run()
        

Training

The training config group contains parameters essential to the training process of the model. This is set by default with modulus_default, but many of the parameters contained in this group are often essential to modify.

• default_training: Default training parameters (set automatically)

Parameters

Some essential parameters that you will find under the training config group include:

• max_steps: Number of training iterations.

• grad_agg_freq: Number of iterations to aggregate gradients over (default is 1). Effectively, setting grad_agg_freq=2 will double the batch size per iteration, compared to a case with no gradient aggregation.

• rec_results_freq: Frequency to record results. This value will be used as the default frequency for recording constraints, validators, inferencers and monitors. See Results Frequency for more details.

• save_network_freq: Frequency to save a network checkpoint.

• amp: Use automatic mixed precision. This will set the precision for GPU operations to improve performance (default is 'float16' set using amp_dtype).

• ntk.use_ntk: Use neural tangent kernel in training (default set to False)

Loss

The loss config group is used to select different loss aggregations that are supported by Modulus Sym. A loss aggregation is the method used to combine the losses from different constraints. Different methods can yield improved performance for some problems.

• sum: Simple summation aggregation (default)

• grad_norm: Gradient normalization for adaptive loss balancing

• homoscedastic: Homoscedastic Task Uncertainty for Loss Weighting

• lr_annealing: Learning Rate Annealing

• soft_adapt: Adaptive loss weighting

• relobralo: Relative loss balancing with random lookback

Optimizer

The loss optimizer group contains the supported optimizers that can be used in Modulus Sym which includes ones that are built into PyTorch as well as from Torch Optimizer package. Some of the most commonly used optimizers include:

• adam: ADAM optimizer

• sgd: Standard stochastic gradient descent

• rmsprop: The RMSProp algorithm

• adahessian: Second order stochastic optimization algorithm

• bfgs: L-BFGS iterative optimization method

as well as these more unique optimizers: a2grad_exp, a2grad_inc, a2grad_uni, accsgd, adabelief, adabound, adadelta, adafactor, adagrad, adamax, adamod, adamp, adamw, aggmo, apollo, asgd, diffgrad, lamb, madgrad, nadam, novograd, pid, qhadam, qhm, radam, ranger, ranger_qh, ranger_va, rmsprop, rprop, sgdp, sgdw, shampoo, sparse_adam, swats, yogi.

Scheduler

The scheduler optimizer group contains the supported learning rate schedulers that can be used in Modulus Sym. By default none is specified for which a constant learning rate will be used.

• exponential_lr: PyTorch exponential learning rate decay initial_learning_rate * gamma ^ (step)

• tf_exponential_lr: Tensorflow parameterization of exponential learning rate decay initial_learning_rate * decay_rate ^ (step / decay_steps)

As previously mentioned, a particular benefit using Hydra configs to control Modulus Sym is that any of these parameters can be controlled through CLI. This can be particularly useful during hyperparameter tuning or queuing up multiple runs using Hydra multirun. Here are a couple of examples which may be particularly useful when developing physics-informed models.

Listing 21 Changing optimizer and learning rate

            

            
$ python main.py optimizer=sgd optimizer.lr=0.01
        

Listing 22 Hyperparameter search over architecture parameters using multirun

            

            
$ python main.py -m arch.fully_connected.layer_size=128,256 arch.fully_connected.nr_layers=2,4,6
        

Listing 23 Training for a different number of iterations

            

            
$ python main.py training.max_steps=1000
        

Results Frequency

Modulus Sym offers several different methods for recording the results of your training including recording validation, inference, batch, and monitor results. Each of these can be individually controlled in the training config group, however, typically it’s preferred for each to have the same frequency. In these instances, the rec_results_freq parameter can be used to control all of these parameters uniformly. The following two config files are equivalent.

            

            
# config/config.yaml
defaults:
    - modulus_default

training:
    rec_results_freq: 1000
    rec_constraint_freq: 2000
        

            

            
# config/config.yaml
defaults:
    - modulus_default

training:
    rec_validation_freq: 1000
    rec_inference_freq: 1000
    rec_monitor_freq: 1000
    rec_constraint_freq: 2000
        

Changing Activation Functions

Activations functions are one of the most important hyperparameters to test for any deep learning model. While all of Modulus Sym’ networks have default activations functions that have been seen to provide the best performance, specific activations may perform better than others on a case to case basis. Changing a activation function is straight forward using the instantiate_arch method:

Listing 24 Initializing a fully-connect model with Tanh activation functions

            

            
# Python code
import modulus.sym
from modulus.sym.hydra import instantiate_arch
from modulus.sym.hydra.config import ModulusConfig
from modulus.sym.models.layers import Activation

@modulus.main(config_path="conf", config_name="config")
def run(cfg: ModulusConfig) -> None:
    model_1 = instantiate_arch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("u"), Key("v")],
        cfg=cfg.arch.fully_connected,
        activation_fn=Activation.TANH,
    )

if __name__ == "__main__":
    run()
        

Many of Modulus Sym’ models also include support for Adaptive Activation Functions which can be turned on in the config file or explicitly in the code:

            

            
# config/config.yaml
defaults:
    - modulus_default
    - arch:
        - fully_connected

arch:
    fully_connected:
        adaptive_activations: true
        

Multiple Architectures

For some problems, its better to have multiple models to learn the solution of different state variables. This may require the use of models that are the same architecture with different hyperparameters. We can have multiple neural network models with the same architecture using config group overrides in Hydra. Here the arch_schema config group is used to access an architecture’s structured config.

Listing 25 Extending configs with customized architectures

            

            
# config/config.yaml
defaults:
    - modulus_default
    - /arch_schema/fully_connected@arch.model1
    - /arch_schema/fully_connected@arch.model2

arch:
    model1:
        layer_size: 128
    model2:
        layer_size: 256
        

Listing 26 Initialization of two custom architectures

            

            
# Python code
import modulus.sym
from modulus.sym.hydra import instantiate_arch
from modulus.sym.hydra.config import ModulusConfig

@modulus.main(config_path="conf", config_name="config")
def run(cfg: ModulusConfig) -> None:
    model_1 = instantiate_arch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("u"), Key("v")],
        cfg=cfg.arch.model1,
    )

    model_2 = instantiate_arch(
        input_keys=[Key("x"), Key("y")],
        output_keys=[Key("u"), Key("v")],
        cfg=cfg.arch.model2,
    )


if __name__ == "__main__":
    run()
        

Run Modes

Modulus Sym has two different run modes available for training and evaluation:

• train: Default run mode. Trains the neural network.

• eval: Evaluates provided inferencers, monitors and validators using the last saved training checkpoint. Useful for post-processing after the training is complete.

Listing 27 Changing run mode to evaluate

            

            
 # config/config.yaml
 defaults:
     - modulus_default

 run_mode: 'eval'
        

Criterion Based Stopping

Modulus Sym supports early training termination, based on a user specified criterion, before the maximum number of iterations is reached.

• metric: Metric to be monitored during the training. This can be the total loss, individual loss terms, validation metrics, or metrics in the monitor domain. For example, in the annular ring example, you can choose loss, loss_continuity, momentum_imbalance, or l2_relative_error_u as the metric. Note the use of l2_relative_error_ for metrics from the validation domain, this is consistent with the tag used for tensorboard plots.

• min_delta: Minimum required change in the metric to qualify as a training improvement.

• patience: Number of training steps to wait for a training improvement to happen.

• mode: Choose ‘min’ if the metric is to be minimized, or ‘max’ if the metric is to be maximized.

• freq: Frequency of evaluating the stop criterion. Note that if using a metric from the validation or monitor domain, freq should be a multiplier of the rec_validation_freq or rec_monitor_freq.

• strict: If True, raises an error in case the metric is not valid.

Listing 28 Defining a stopping criterion for training

            

            
 # config/config.yaml
 defaults:
     - modulus_default

 stop_criterion:
     - metric: 'l2_relative_error_u'
     - min_delta: 0.1
     - patience: 5000
     - mode: 'min'
     - freq: 2000
     - strict: true
        

When using a metric from the validation domain, criterion based stopping can also serve as an early stopping regularization method for data-driven models.