For geohazards and geotechnics, numerous problems involve large deformation, such as installation of foundations, landslides, debris flow, collapses of excavation and tunnel and the formation sinkhole. Benefitted from the sustained development of computing power, numerical simulations have become standard methods in geomechanics and its related fields. Among those numerical methods, the finite element method (FEM) features prominently in engineering practices. For FEM, however, excessive deformation of a mesh can result in numerical inaccuracies, even to the point of making calculation impossible for large deformation problems.

Partial Differential Equations (PDEs) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In order to solve PDEs that represent real systems to an acceptable degree, analytical methods are usually not enough. One has to resort to discretization methods. For engineering problems, probably the best known option is the Finite Element Method (FEM). However, powerful alternatives such as mesh-ree methods, Isogeometric Analysis (IGA) or Finite Difference Methods (FDM) are also available, just to name a few. A new route to solve PDEs is so called physics-informed neural networks that make use of machine learning based activation functions as approximators. There is great flexibility to define their structure and important advances in the architecture and the efficiency of the algorithms to implement them make such approaches a very interesting alternative to “classical” methods such as FEM.

The proposed topic on rail transportation noise and vibration covers the broad issue of generation and propagation of sound and ground borne vibration from rail transport. Rail induced vibration has gained more attention in recent years. This Special Issue is partly dedicated, but not limited, to the urban environment, with low speed rail bound transport. In addition, airborne and ground-borne noise from urban light rail transit (LRT) networks is considered a major parameter of possible degradation of the urban acoustic environment.

Constitutive models based on mechanics theories have been the kernel of performance prediction of transport infrastructures and materials. They lay down a solid foundation for material selection, design and infrastructural evaluation and maintenance decisions. Advances in mechanics modelling for the transport infrastructures and construction materials are emerging constantly such as the nonlinear viscoelasticity, viscoplasticity, fracture, and damage mechanics models. Meanwhile, various numerical modelling technologies are being developed and implemented to solve the multiscale and multiphysics equations and models for the transport infrastructure and materials.