diff --git a/_publications/34-Wu_JChemPhys_2024.md b/_publications/34-Wu_JChemPhys_2024.md
index 7b7ed69bacac3..f8d90118bea61 100644
--- a/_publications/34-Wu_JChemPhys_2024.md
+++ b/_publications/34-Wu_JChemPhys_2024.md
@@ -6,7 +6,8 @@ excerpt: 'We reveal that the fitting errors in the machine-learned forces agains
 date: 2024-07-01
 venue: 'The Journal of Chemical Physics'
 ---
-![image](https://github.com/hityingph/hityingph.github.io/assets/54773018/fc7e09c1-7898-453c-847f-2744a60c2318)
+![Uploading 8bdb7b53dab6327d9f21348c98c3a9f.jpg…]()
+
 
 Machine learned potentials (MLPs) have been widely employed in molecular dynamics simulations to study thermal transport. However, the literature results indicate that MLPs generally underestimate the lattice thermal conductivity (LTC) of typical solids. Here, we quantitatively analyze this underestimation in the context of the neuroevolution potential (NEP), which is a representative MLP that balances efficiency and accuracy. Taking crystalline silicon, gallium arsenide, graphene, and lead telluride as examples, we reveal that the fitting errors in the machine-learned forces against the reference ones are responsible for the underestimated LTC as they constitute external perturbations to the interatomic forces. Since the force errors of a NEP model and the random forces in the Langevin thermostat both follow a Gaussian distribution, we propose an approach to correcting the LTC by intentionally introducing different levels of force noises via the Langevin thermostat and then extrapolating to the limit of zero force error. Excellent agreement with experiments is obtained by using this correction for all the prototypical materials over a wide range of temperatures. Based on spectral analyses, we find that the LTC underestimation mainly arises from increased phonon scatterings in the low-frequency region caused by the random force errors.
 
@@ -14,4 +15,4 @@ Machine learned potentials (MLPs) have been widely employed in molecular dynamic
 
 [Download SI here](https://doi.org/10.1063/5.0213811)
 
-[Download reeference datasets and MLPs here](https://github.com/hityingph/supporting-info)
\ No newline at end of file
+[Download reeference datasets and MLPs here](https://github.com/hityingph/supporting-info)