Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2401.05439

Physics-informed Deep Learning to Solve Three-dimensional Terzaghi Consolidation Equation: Forward and Inverse Problems

Biao Yuan·Ana Heitor·He Wang·Xiaohui Chen
View original source ↗Read source document ↗Export metadata ↓

Abstract

The emergence of neural networks constrained by physical governing equations has sparked a new trend in deep learning research, which is known as Physics-Informed Neural Networks (PINNs). However, solving high-dimensional problems with PINNs is still a substantial challenge, the space complexity brings difficulty to solving large multidirectional problems. In this paper, a novel PINN framework to quickly predict several three-dimensional Terzaghi consolidation cases under different conditions is proposed. Meanwhile, the loss functions for different cases are introduced, and their differences in three-dimensional consolidation problems are highlighted. The tuning strategies for the PINNs framework for three-dimensional consolidation problems are introduced. Then, the performance of PINNs is tested and compared with traditional numerical methods adopted in forward problems, and the coefficients of consolidation and the impact of noisy data in inverse problems are identified. Finally, the results are summarized and presented from three-dimensional simulations of PINNs, which show an accuracy rate of over 99% compared with ground truth for both forward and inverse problems. These results are desirable with good accuracy and can be used for soil settlement prediction, which demonstrates that the proposed PINNs framework can learn the three-dimensional consolidation PDE well. Keywords: Three-dimensional Terzaghi consolidation; Physics-informed neural networks (PINNs); Forward problems; Inverse problems; soil settlement

Explore related subjects

cs.LGcs.CE

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Biao Yuan, Ana Heitor, He Wang, Xiaohui Chen. 2024-01-08. Physics-informed Deep Learning to Solve Three-dimensional Terzaghi Consolidation Equation: Forward and Inverse Problems. https://doi.org/10.1007/s13369-025-10602-2

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

AUC Maximization from Biased Positive-unlabeled Data with Confidence

Maximizing the area under the receiver operating characteristic curve (AUC) is a standard approach to imbalanced binary classification. Although positive and negative data are required for maximizing the AUC, negative data are often difficult to collect in some real-world applications due to privacy concerns or the need for specialized expertise to annotate them. Thus, AUC maximization from positive and unlabeled (PU) data has been attracting attention. Existing methods assume that labeled positive data are unbiased samples from the true positive distribution. However, this ideal assumption is often violated in practice. In this paper, we propose a method to maximize the AUC from biased PU data. To address the bias, our key idea is to exploit {\it confidence}, i.e., the probability that an instance is positive, associated with the small number of labeled positive data. We derive an estimator of the AUC risk using biased PU data with confidence, enabling AUC maximization under such bias. We further show that the rewritten AUC risk induces a Bayes-optimal AUC ranking even when the available confidence is any strictly increasing transformation of the true posterior probability. We experimentally show the effectiveness of our method on eight real-world datasets.

cs.LG↗
arXiv2026

Measuring the Value of World-Model Updates: A Counterfactual Utility Protocol for Continual Adaptation

Continual world models must decide whether new data justify changing the model. Fixed replay schedules and prediction-error triggers specify when to update, but neither reveals the value of an individual update: one deployment run cannot show how the same model would have performed at that moment had it held its parameters. We introduce the fork ledger, which branches a deployment stream at pre-registered decision points into matched update and hold continuations under common random numbers. It evaluates both continuations on the same episodes and records $\Delta R = R_{\mathrm{update}} - R_{\mathrm{hold}}$. Always applying one fixed update mechanism lowers return on all three simulated control tasks: CartPole ($-144.0$; checkpoint-bootstrap $95\%$ CI $[-185.4,-116.1]$, against a converged return near $650$), Walker ($-82.8$; $[-101.1,-61.7]$) and Cheetah ($-18.6$; $[-29.0,-6.6]$). Divergence is an outcome of applying the update, so the estimand counts every attempted fork; restricted to the $693$ of $720$ that did not collapse, CartPole and Walker are unchanged in sign ($-113.4$ and $-82.1$) and Cheetah becomes unresolved ($-3.9$; $[-17.5,+13.0]$). The task is the unit of inference: each contributes $240$ attempted forks over five pretrained checkpoints crossed with two drift directions. The ledger makes counterfactual utility observable for a fixed mechanism, allowing triggers to be judged by the updates they select rather than by surprise detection alone.

cs.LG↗
arXiv2026

When More Is Not Better: Component Anti-Synergy in a P300 Speller

P300 brain-computer interface (BCI) spellers can provide hands-free communication for people with severe motor impairments. Modern pipelines combine multiple individually promising components, often assuming that 'more-is-better'. We tested this assumption using a four-component full-factorial experiment varying the inclusion of Euclidean Alignment (EA), xDAWN spatial filtering, subject calibration, and language model priors on a public P300 dataset. Performance was evaluated using accuracy, repetitions, and information transfer rate (ITR) with mixed-effects models. Results show that the value of components is conditional rather than additive. Calibration was the strongest singular contributor, while EA compensated for its absence in zero-calibration settings. Adding independently useful components could also reduce performance, revealing component anti-synergy. Contrary to conventional wisdom, LM support was not universally beneficial: its effect depends strongly on the strength of the underlying EEG pipeline, while results from a larger LM showed a similar pattern. Together, these findings challenge maximal 'all-on' pipeline design and highlight the value of selecting spatial and language-support components according to the quality of available EEG evidence.

cs.LG↗