# An improved data-free surrogate model for solving partial differential equations using deep neural networks

> Research article (Scientific Reports, 2021) · cited 40× · AI/ML

**Wikidata**: [openalex:W3202567723](https://www.wikidata.org/wiki/openalex:W3202567723)  
**Source**: https://4ort.xyz/entity/an-improved-data-free-surrogate-model-for-solving-partial-differential-equations-using-deep-neural-networks