# Lagged backward-compatible physics-informed neural networks for unsaturated soil consolidation analysis

arXiv: https://arxiv.org/abs/2602.07031 · HTML: https://mlsanity.com/paper/2602.07031/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 55 references that are in the map.
- First posted on arXiv 3 Feb 2026.

## Builds on (most cited first, 8 of 8)

- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Automatic differentiation in machine learning: a survey](https://mlsanity.com/paper/1502.05767/) (2015)
- [When and why PINNs fail to train: A neural tangent kernel perspective](https://mlsanity.com/paper/2007.14527/) (2020)
- [DeepXDE: A deep learning library for solving differential equations](https://mlsanity.com/paper/1907.04502/) (2019)
- [Physics-informed neural networks (PINNs) for fluid mechanics: A review](https://mlsanity.com/paper/2105.09506/) (2021)
- [Activation Functions in Deep Learning: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2109.14545/) (2021)
- [Transfer learning enhanced physics informed neural network for phase-field modeling of fracture](https://mlsanity.com/paper/1907.02531/) (2019)
- [Deep Learning for One-dimensional Consolidation](https://mlsanity.com/paper/2004.11689/) (2020)

## Built on by (most cited first, 2 of 2)

- [Physics-Informed Neural Networks for Radial Consolidation of Combined Electroosmotic, Vacuum and Surcharge Preloading Considering Smear Effects](https://mlsanity.com/paper/2606.00056/) (2026)
- [Physics-Informed Neural Network Modeling of Biodegradable Contaminant Transport through GCL/SL Composite Liners](https://mlsanity.com/paper/2606.04392/) (2026)

## Abstract (arXiv)

This study develops a Lagged Backward-Compatible Physics-Informed Neural Network (LBC-PINN) for simulating and inverting one-dimensional unsaturated soil consolidation under long-term loading. To address the challenges of coupled air and water pressure dissipation across multi-scale time domains, the framework integrates logarithmic time segmentation, lagged compatibility loss enforcement, and segment-wise transfer learning. In forward analysis, the LBC-PINN with recommended segmentation schemes accurately predicts pore air and pore water pressure evolution. Model predictions are validated against finite element method (FEM) results, with mean absolute errors below 1e-2 for time durations up to 1e10 seconds. A simplified segmentation strategy based on the characteristic air-phase dissipation time improves computational efficiency while preserving predictive accuracy. Sensitivity analyses confirm the robustness of the framework across air-to-water permeability ratios ranging from 1e-3 to 1e3.