MatPL Parameters

This section describes user-configurable parameters for all models. Basic parameters must be supplied, while advanced parameters have defaults that can be overridden in JSON. A relative path is resolved from the current working directory; an absolute path begins at the filesystem root.

Basic Parameters

model_type

Selects the model type: LINEAR, NN, DP, or NEP.

atom_type

Sets the elements in any chosen order using atomic numbers or symbols. Examples: [29] or ["Cu"] for copper, and [1,6] or ["H","C"] for CH4.

train_data

Specifies training-data paths, either relative or absolute.

• DP and NEP support extxyz, pwmlff/npy, deepmd/npy, deepmd/raw, pwmat/movement, vasp/outcar, and cp2k/md.
• LINEAR and NN support only pwmat/movement.

valid_data

Specifies validation-data paths, either relative or absolute.

• DP and NEP support extxyz, pwmlff/npy, deepmd/npy, deepmd/raw, pwmat/movement, vasp/outcar, and cp2k/md.
• LINEAR and NN support only pwmat/movement.

test_data

Specifies test-data paths for the test command, either relative or absolute.

• DP and NEP support extxyz, pwmlff/npy, deepmd/npy, deepmd/raw, pwmat/movement, vasp/outcar, and cp2k/md.
• LINEAR and NN support only pwmat/movement.

format

Sets the format of train_data, valid_data, and test_data. Supported values include extxyz, pwmlff/npy, deepmd/npy, deepmd/raw, and direct trajectory formats pwmat/movement, vasp/outcar, and cp2k/md. The default is pwmat/movement. See pwdata.

info

All input datasets must use the same format.

model_load_file

• For fine-tuning or continued training, specifies an initial .ckpt model.
• For test, specifies the model path, either relative or absolute.

nep_txt_file

• For fine-tuning or continued training, specifies a .txt model such as GPUMD nep4.txt or nep5.txt.
• The text file may be a universal force field covering 89 elements. MatPL extracts parameters for the elements in atom_type, enabling fine-tuning to a smaller model. This can be combined with fix_cij, fix_hiddenlayer, and fix_outlayer under model->fitting_net.

recover_train

Whether to resume an interrupted training task. The default is true.

reserve_work_dir

For LINEAR and NN, whether to retain work_dir after execution. The default is false.

save_step

Sets the model-save interval in iterations. The default is None, so models are saved only after each epoch.

max_save_num

With save_step, sets the maximum number of recent models retained. The default is 10.

NEP Model Hyperparameters

The complete NEP model configuration is:

    "model": {
        "descriptor": {
            "cutoff": [6.0,6.0],
            "n_max": [4,4],
            "basis_size": [12,12],
            "l_max": [4,2,1],
            "zbl": 2.0
        },
        "fitting_net": {
            "network_size": 40,
            "fix_cij":false,
            "fix_hiddenlayer":false,
            "fix_outlayer":false
        }
    }

cutoff

Sets radial and angular cutoff radii. The default is [8.0, 4.0].

n_max

Sets n_max for radial and angular descriptors. Each value must be between 0 and 19. The default is [4,4].

basis_size

Sets the radial and angular basis sizes. Each value must be between 0 and 19. The default is [8,8].

l_max

Sets angular expansion orders and enables four- and five-body descriptors. The default [4,2,1] contains the three-, four-, and five-body orders. Use [4,0,0] for three-body only or [4,2,0] for three- and four-body descriptors.

info

The numbers of two-, three-, four-, and five-body descriptors are n_max[0]+1, (n_max[1]+1)*l_max[0], n_max[1]+1, and n_max[1]+1, respectively.

network_size

Sets the number of neurons in NEP's single hidden layer. The default is 40.

zbl

Sets the outer cutoff of the Ziegler–Biersack–Littmark (ZBL) potential (DOI: 10.1007/978-1-4615-8103-1_3); the inner cutoff is fixed at half the outer cutoff. It is disabled by default. A value in $1.0 \le zbl \le 3.0$ is recommended.

use_typewise_cutoff_zbl

Enables type-wise ZBL cutoffs. The outer cutoff for a pair is min(zbl, use_typewise_cutoff_zbl × sum of covalent radii), and the inner cutoff is fixed at 0.0. Disabled by default; introduced in MatPL-2026.3 Update 1.

fix_cij

Fine-tuning option that freezes NEP two- and three-body feature coefficients. The default is false.

fix_hiddenlayer

Fine-tuning option that freezes NEP hidden-layer parameters W0 and B0. The default is false.

fix_outlayer

Fine-tuning option that freezes NEP output-layer parameters W1 and B1. The default is false.

Interpreting NEP.txt

A standard NEP.txt header is shown below.

nep5   2 O Hf           # Number of element types, followed by their symbols
zbl 1 2                 # Present only when ZBL is enabled during training
cutoff 6.0 6.0 108 108  # Two-body cutoff, many-body cutoff, and their maximum neighbor counts
n_max  4 4              # Two-body and many-body n_max
basis_size 12 12        # Two-body and many-body basis_size
l_max  4 2 1            # Three-, four-, and five-body l_max values
ANN    40 0             # 40 hidden neurons; 0 is a placeholder

The remaining lines contain four blocks: network parameters, two-body coefficients, three-body coefficients, and normalization values.

• Block 1 contains network parameters for $E_i=\tanh(q_nW0+B0)W1+b1$. Its size is number of elements × (number of features × ANN[0] + ANN[0] + ANN[0]) + number of elements. For each element in header order, it stores W0, B0, and W1, followed by one b1 per element. A GPUMD-trained NEP4 file stores only one b1, the mean across elements. W0 is flattened row-major from [ANN hidden units, number of features].

• Block 2 contains two-body coefficients: number of elements² × (n_max[0]+1) × (basis_size[0]+1).

• Block 3 contains three-body coefficients: number of elements² × (n_max[1]+1) × (basis_size[1]+1).

  In either coefficient block, the matrix order is [I,J,N,K]: I is the central element, J is the neighbor element, both following header order; N=n_max+1; and K=basis_size+1.

• Block 4 contains one normalization value per feature, ordered by two-, three-, four-, and five-body terms. Their counts are n_max[0]+1, (n_max[1]+1)*l_max[0], n_max[1]+1, and n_max[1]+1.

DP Model Hyperparameters

The complete DP model configuration is:

    "type_embedding":false,
    "model": {
        "type_embedding":{
            "physical_property":["atomic_number", "atom_mass", "atom_radius", "molar_vol", "melting_point", "boiling_point", "electron_affin", "pauling"]
        },
        "descriptor": {
            "Rmax": 6.0,
            "Rmin": 0.5,
            "M2": 16,
            "network_size": [25,25,25]
        },
        "fitting_net": {
            "network_size": [50,50,50,1]
        }
    }

type_embedding

Configures type embedding for DP training. You may also set "type_embedding":true alongside model, which uses ["atomic_number","atom_radius","atom_mass","electron_affin","pauling"]. The default is false.

physical_property

Selects physical properties for DP type embedding. Eight properties are available:

• atomic_number: atomic number
• atom_mass: atomic mass
• atom_radius: atomic radius
• molar_vol: molar volume
• melting_point: melting point
• boiling_point: boiling point
• electron_affin: electron affinity
• pauling: Pauling electronegativity

The default physical_property is ["atomic_number","atom_radius","atom_mass","electron_affin","pauling"].

Rmax

Maximum cutoff radius of the DP smoothing function. The default is $6.0 \text{\AA}$.

Rmin

Minimum cutoff radius of the DP smoothing function. The default is $0.5 \text{\AA}$.

M2

Sets the DP embedding-network output dimension and therefore the fitting-network input dimension. In the example, these are 25 × 16 and 25 × 16 = 400. The default is 16.

network_size

Sets the embedding- and fitting-network structures. Defaults are [25,25,25] and [50,50,50,1].

Embedding network: Input -> hidden layer 1 (25 neurons) -> hidden layer 2 (25 neurons) -> output layer (25 neurons)

Fitting network: Input (M2 × 25) -> three hidden layers (50 neurons each) -> output (1 neuron)

NN Model Hyperparameters

The complete NN model configuration is:

    "model": {
        "descriptor": {
            "Rmax": 6.0,
            "Rmin": 0.5,
            "feature_type": [3,4]
        },
        "fitting_net": {
            "network_size": [15,15,1]
        }
    }

Rmax

Maximum feature cutoff radius. The default is $6.0 \text{\AA}$.

Rmin

Minimum feature cutoff radius. The default is $0.5 \text{\AA}$.

feature_type

Selects feature types. Supported values are [1,2], [3,4], [5], [6], [7], and [8]. The default [3,4] selects two- and three-body Gaussian features. See Appendix 1.

network_size

Sets the fitting-network structure. The default [15,15,1] gives: Input -> hidden layer 1 (15 neurons) -> hidden layer 2 (15 neurons) -> output (1 neuron)

Linear Model Hyperparameters

The complete Linear model configuration is:

    "model": {
        "descriptor": {
            "Rmax": 6.0,
            "Rmin": 0.5,
            "feature_type": [3,4]
        }
    }

Rmax

Maximum feature cutoff radius. The default is $6.0 \text{\AA}$.

Rmin

Minimum feature cutoff radius. The default is $0.5 \text{\AA}$.

feature_type

Selects feature types using the same settings as the NN model. Supported values are [1,2], [3,4], [5], [6], [7], and [8]. The default [3,4] selects two- and three-body Gaussian features. See Appendix 1.

ADAM Optimizer Hyperparameters

The complete ADAM configuration is:

    "optimizer": {
        "optimizer": "ADAM",
        "epochs": 30,
        "reset_epoch":false,
        "batch_size": 1,
        "print_freq": 10,
        "lambda_2" : 0.1,
        "learning_rate": 0.001,
        "stop_lr": 3.51e-08,
        "stop_step": 1000000,
        "decay_step": 5000,
        "max_norm": 0.5,
        "norm_type": 2,
        "t_0": 6,
        "t_mult": 1,
        "train_energy": true,
        "train_force": true,
        "train_virial": false,
        "start_pre_fac_force": 1000,
        "start_pre_fac_etot": 0.02,
        "start_pre_fac_virial": 50.0,
        "end_pre_fac_force": 1.0,
        "end_pre_fac_etot": 1.0,
        "end_pre_fac_virial": 1.0
    }

optimizer

Selects the optimizer. The default is ADAM; use LKF for the LKF optimizer. See the LKF paper.

reset_epoch

Whether restarted training begins at epoch 0. The default is true. Set false to resume from a checkpoint and restore ADAM's first- and second-moment states.

epochs

Sets the number of epochs. Each epoch processes the entire dataset in mini-batches with forward propagation, loss calculation, and backpropagation. The default is 30.

Choose the epoch count by monitoring training and validation. Too few epochs may underfit; too many may overfit and reduce generalization.

batch_size

Sets the number of samples in each mini-batch. The default is 1.

print_freq

Sets the number of mini-batch iterations between training-error reports. The default is 10.

train_energy

Whether to train on total energy. The default is true.

train_force

Whether to train on forces. The default is true.

train_virial

Whether to train on virials. The default is false.

lambda_2

Sets ADAM L2 regularization. It is disabled by default and may reduce overfitting.

learning_rate

Initial ADAM learning rate. The default is 0.001.

stop_lr

Minimum learning rate. Once reached, it remains fixed. The default is 3.51e-08.

stop_step

Step at which learning-rate decay stops and the rate equals stop_lr. The default is 1000000.

decay_step

Learning-rate decay interval. The default is 5000 steps.

learning_rate, stop_lr, stop_step, and decay_step determine the schedule as follows:

decay_rate = np.exp(np.log(stop_lr/learning_rate) / (stop_step/decay_step))
real_lr = learning_rate * np.power(decay_rate, (iter_num//decay_step))

First calculate decay_rate:

$$\text{decay\_rate} = \exp\left(\frac{\log(\text{stop\_lr}/\text{start\_lr})}{\text{stop\_step}/\text{decay\_step}}\right)$$

Then update the learning rate:

$$\text{real\_lr} = \text{start\_lr} \cdot \text{decay\_rate}^{\lfloor \text{iter\_num}/\text{decay\_step} \rfloor}$$

where iter_num is the training iteration.

Energy and Force Prefactors in the Loss

Force, energy, and virial prefactors:

• start_pre_fac_force: force-loss prefactor at the start of training. Must be nonnegative; default 100.

• end_pre_fac_force: force-loss prefactor at the end of training. Default 1.0.

• start_pre_fac_etot: total-energy prefactor at the start of training. Default 1.0.

• end_pre_fac_etot: total-energy prefactor at the end of training. Default 1.0.

• start_pre_fac_virial: virial prefactor at the start of training. Default 0.1.

• end_pre_fac_virial: virial prefactor at the end of training. Default 0.1.

Loss-prefactor calculation:

During ADAM training, each loss prefactor depends on the current real_lr:

lr_ratio = real_lr / learning_rate
lr_ratio = min(max(lr_ratio, 0.0), 1.0)

prefactor = end_prefactor + (start_prefactor - end_prefactor) * lr_ratio

Equivalently:

$$r = \mathrm{clip} \left( \frac{\text{real\_lr}}{\text{learning\_rate}}, 0, 1 \right)$$ $$p_x = p_x^{\mathrm{end}} + \left( p_x^{\mathrm{start}} - p_x^{\mathrm{end}} \right) r$$

where x may be force, etot, or virial. At the start of training:

$$\text{real\_lr} \approx \text{learning\_rate}, \quad r \approx 1$$

Therefore:

$$p_x \approx p_x^{\mathrm{start}}$$

Later, as the learning rate decreases:

$$\text{real\_lr} \to 0, \quad r \to 0$$

Therefore:

$$p_x \to p_x^{\mathrm{end}}$$

Loss formula:

Total loss combines enabled force, total-energy, and virial terms:

$$L = p_F L_F^{\mathrm{MSE}} + p_{\mathrm{etot}} \frac{L_{\mathrm{Etot}}^{\mathrm{MSE}}}{N_{\mathrm{avg}}} + p_{\mathrm{virial}} \frac{L_{\mathrm{Virial}}^{\mathrm{MSE}}}{N_{\mathrm{avg}}}$$

• Each term uses MSELoss:

$$L_{\mathrm{}}^{\mathrm{MSE}} = \frac{1}{n}\sum_{i}^{n}\left(Y_i-\hat{Y_i}\right)^2$$

• $L_F$ is force loss.
• $L_{Etot}$ is total-energy loss.
• $L_{Virial}$ is total-virial loss.
• $N_{\mathrm{avg}}$ is the mean atom count per structure in the current batch.
• $p_F$, $p_{Etot}$, and $p_{Virial}$ are the corresponding prefactors.

Because Etot and Virial are structure-level totals, dividing them by N_avg makes their scale closer to per-atom quantities and prevents larger systems from receiving inherently greater weight.

Gradient Clipping

Norm-Based Clipping: max_norm and norm_type

max_norm and norm_type configure norm-based clipping. The default max_norm=None disables it.

If the norm of all parameter gradients exceeds max_norm, gradients are scaled proportionally until the norm equals max_norm.

This preserves relative gradient directions while preventing exploding gradients. norm_type selects the norm.

norm_type is integer 1 for L1 or 2 for L2. The default is 2.

The L1 norm is the sum of absolute gradient values: $\|g\|_1 = \sum_{i=1}^{n} |g_i|$， If $\|g\|_1 > \text{max\_norm}$, gradients are scaled to

$$g_{\text{clipped}} = g \cdot \frac{\text{max\_norm}}{\|g\|_1}$$

The L2 norm is the Euclidean gradient norm: $\|g\|_2 = \sqrt{\sum_{i=1}^{n} g_i^2}$， If $\|g\|_2 > \text{max\_norm}$, gradients are scaled to

$$g_{\text{clipped}} = g \cdot \frac{\text{max\_norm}}{\|g\|_2}$$

Value-Based Clipping: clip_value

Clips each gradient component to [-clip_value, clip_value]. The default None disables it.

$$g_i^{\text{(clipped)}} = \begin{cases} \text{clip\_value}, & \text{if } g_i > \text{clip\_value} \\ -\text{clip\_value}, & \text{if } g_i < -\text{clip\_value} \\ g_i, & \text{otherwise} \end{cases}$$

Cosine Annealing with Warm Restarts: t_0 and t_mult

Positive integers t_0 and t_mult enable cosine annealing with warm restarts for ADAM. Once enabled, optim.lr_scheduler.CosineAnnealingWarmRestarts controls the learning rate and the decay_step schedule is disabled.

• t_0: length of the first cycle, in epochs.

• t_mult: factor by which the cycle length grows after each restart.

• The epoch $E_n$ at which cycle $n$ ends and the learning rate reaches its minimum is calculated as follows:

  • For t_mult = 1, cycles have fixed length t_0.

  • For t_mult > 1, cycle lengths grow geometrically:

  $E_n = t_0 \times \frac{T_{mult}^n - 1}{T_{mult} - 1} \quad (n = 1, 2, 3, \dots)$

• When cosine annealing is enabled, the model at each $E_n$, immediately before restart, is saved under model_record/saved_models.

In the figure below, learning_rate is 0.001, t_0=1, t_mult=2, and stop_lr is 3.51e-08. Restarts occur at epochs 1, 3, 7, 15, and so on.

Statistics of the first five restart epochs for each group

Combination (T_0, T_mult)	1st restart	2nd restart	3rd restart	4th restart	5th restart
(1, 2)	1	3	7	15	31
(1, 6)	1	7	43	259	1555
(2, 2)	2	6	14	30	62
(2, 4)	2	10	42	170	682
(2, 1)	2	4	6	8	10

Detailed calculation process

1. (1, 2): The cycle lengths are 1, 2, 4, 8, 16... respectively
   → Restart points: 1, 1+2=3, 3+4=7, 7+8=15, 15+16=31

2. (1, 6): The cycle lengths are 1, 6, 36, 216, 1296... respectively
   → Restart points: 1, 1+6=7, 7+36=43, 43+216=259, 259+1296=1555

3. (2, 2): The cycle lengths are 2, 4, 8, 16, 32... respectively
   → Restart points: 2, 2+4=6, 6+8=14, 14+16=30, 30+32=62

4. (2, 4): The cycle lengths are 2, 8, 32, 128, 512... respectively
   → Restart points: 2, 2+8=10, 10+32=42, 42+128=170, 170+512=682

5. (2, 1): The cycle length is constant at 2, 2, 2, 2, 2...
   → Restart points: 2, 4, 6, 8, 10 (arithmetic progression)

Learning-Rate Scaling

scale_lr controls scaling by batch size and GPU count. The default is false, so the effective rate equals learning_rate.

When enabled, the default sqrt scaling is

$$\mathrm{real\_lr}=\mathrm{learning\_rate}\times\sqrt{\mathrm{batch\_size}\times N_{\mathrm{GPU}}}$$

"scale_lr": true,
"scaling_method": "sqrt"

This applies to ADAM, ADAMW, and SGD. Increasing batch size or GPU count increases the effective learning rate.

KF Optimizer Hyperparameters

The complete KF configuration is:

    "optimizer": {
        "optimizer": "LKF",
        "epochs": 30,
        "batch_size": 1,
        "print_freq": 10,
        "block_size": 5120,
        "p0_weight": 0.01,
        "kalman_lambda": 0.98,
        "kalman_nue": 0.9987,
        "train_energy": true,
        "train_force": true,
        "train_virial": false,
        "pre_fac_force": 2.0,
        "pre_fac_etot": 1.0,
        "pre_fac_virial": 1.0
    }

optimizer, epochs, batch_size, print_freq, train_energy, train_force, and train_virial have the same meanings as for ADAM.

block_size

Sets the block size of LKF covariance matrix P. Larger blocks consume more memory and train more slowly; smaller blocks may reduce convergence speed and accuracy. The default is 5120; 10240 is recommended for A100 or H100 GPUs.

p0_weight

LKF regularization parameter. The default 0.01 reduces overfitting and must be below 1; setting it to 1 disables regularization.

kalman_lambda

LKF memory factor controlling the weight of previous data. Larger values retain more history. The default is 0.98.

kalman_nue

LKF forgetting rate controlling how quickly kalman_lambda changes. The default is 0.9987.

pre_fac_etot

Weight of total energy in the loss. The default is 1.0.

pre_fac_force

Weight of force in the loss. The default is 2.0.

pre_fac_virial

Weight of virial in the loss. The default is 1.0.

caution

1. Multi-GPU NEP training does not support LKF or GKF.

2. The size of covariance matrix P scales with the square of N/block_size, where N is the parameter count. Training many element types can therefore exhaust GPU memory and converge slowly.