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Fit energy

In this section, we will take $deepmd_source_dir/examples/water/se_e2_a/input.json as an example of the input file.

The fitting network

The construction of the fitting net is given by section {ref}fitting_net <model/fitting_net>

	"fitting_net" : {
	    "neuron":		[240, 240, 240],
	    "resnet_dt":	true,
	    "seed":		1
	},
  • {ref}neuron <model/fitting_net[ener]/neuron> specifies the size of the fitting net. If two neighboring layers are of the same size, then a ResNet architecture is built between them.
  • If the option {ref}resnet_dt <model/fitting_net[ener]/resnet_dt> is set to true, then a timestep is used in the ResNet.
  • {ref}seed <model/fitting_net[ener]/seed> gives the random seed that is used to generate random numbers when initializing the model parameters.

Loss

The loss function $L$ for training energy is given by

$$L = p_e L_e + p_f L_f + p_v L_v$$

where $L_e$, $L_f$, and $L_v$ denote the loss in energy, forces and virials, respectively. $p_e$, $p_f$, and $p_v$ give the prefactors of the energy, force and virial losses. The prefectors may not be a constant, rather it changes linearly with the learning rate. Taking the force prefactor for example, at training step $t$, it is given by

$$p_f(t) = p_f^0 \frac{ \alpha(t) }{ \alpha(0) } + p_f^\infty ( 1 - \frac{ \alpha(t) }{ \alpha(0) })$$

where $\alpha(t)$ denotes the learning rate at step $t$. $p_f^0$ and $p_f^\infty$ specifies the $p_f$ at the start of the training and the limit of $t \to \infty$ (set by {ref}start_pref_f <loss[ener]/start_pref_f> and {ref}limit_pref_f <loss[ener]/limit_pref_f>, respectively), i.e.

$$pref_f(t) = start_pref_f * ( lr(t) / start_lr ) + limit_pref_f * ( 1 - lr(t) / start_lr )$$

The {ref}loss <loss> section in the input.json is

    "loss" : {
	"start_pref_e":	0.02,
	"limit_pref_e":	1,
	"start_pref_f":	1000,
	"limit_pref_f":	1,
	"start_pref_v":	0,
	"limit_pref_v":	0
    }

The options {ref}start_pref_e <loss[ener]/start_pref_e>, {ref}limit_pref_e <loss[ener]/limit_pref_e>, {ref}start_pref_f <loss[ener]/start_pref_f>, {ref}limit_pref_f <loss[ener]/limit_pref_f>, {ref}start_pref_v <loss[ener]/start_pref_v> and {ref}limit_pref_v <loss[ener]/limit_pref_v> determine the start and limit prefactors of energy, force and virial, respectively.

If one does not want to train with virial, then he/she may set the virial prefactors {ref}start_pref_v <loss[ener]/start_pref_v> and {ref}limit_pref_v <loss[ener]/limit_pref_v> to 0.