About optimal loss function for training physics-informed neural networks under respecting causality

A method is presented that allows to reduce a problem described by differential equations with initial and boundary conditions to the problem described only by differential equations. The advantage of using the modified problem for physics-informed neural networks (PINNs) methodology is that it becomes possible to represent the loss function in the form of a single term associated with differential equations, thus eliminating the need to tune the scaling coefficients for the terms related to boundary and initial conditions. The weighted loss functions respecting causality were modified and new weighted loss functions based on generalized functions are derived. Numerical experiments have been carried out for a number of problems, demonstrating the accuracy of the proposed methods.Comment: 25 pages, 7 figures, 6 table

Problems of wave dynamics of the systems that support moving loads

The work is devoted to the study of the stability of mechanical systems with moving loads. We consider lumped objects that move uniformly along the distributed elastic systems. For example, sliding train supports vibrating, excited in the rails elastic waves, which can lead to instability

Problems of wave dynamics of the systems that support moving loads

The work is devoted to the study of the stability of mechanical systems with moving loads. We consider lumped objects that move uniformly along the distributed elastic systems. For example, sliding train supports vibrating, excited in the rails elastic waves, which can lead to instability

Nonlinear Spatial Localized Strain Waves

A possible way of study of single waves in solids is discussed. The soliton is one of these waves without shape and parameters varying. Soliton deformation parameters are connected with the elastic moduli of the third order that allows defining values of these moduli by means of the measured solitondeformation parameters in various type waveguides made of the same material. The conditions under which a soliton can exist in a rod are analytically determined. For simultaneous excitation of loading in several wave guides two new energetic photosensitive structures (the mixtures are given) initiated by means of short light impulses of noncoherent light sources are proposed. Conditions of excitation of the waves on the basis of multipoint optical initiation loading impulses are described. As a technique for registration the shadowgraph visualization is proposed. It is discussed, how the problem connected to the use of energetic initiation structures consisting in the power background illumination can be solved. The shadow scheme with the use of a tiny dot explosive light source (Tbr ~41 kK) allows to carry out modelling experiments on research of slabbing actions, jet formations, fluffings, hydrodynamic instability during shock-wave loading of investigated samples, which makes it attractive for determination of parameters in equations-of-state for investigated materials, creation of numerical models and their validation. Some examples showing basic possibility of application of the declared techniques are included

Localized nonlinear waves in a semiconductor with charged dislocations

To describe a nonlinear ultrasonic wave in a semiconductor with charged dislocations, an evolution equation is obtained that generalizes the well-known equations of wave dynamics: Burgers and Korteweg de Vries. By the method of truncated decompositions, an exact analytical solution of the evolution equation with a kink profile has been found. The kind of kink (increasing, decreasing) and its polarity depend on the values of the parameters and their signs. An ultrasonic wave in a semiconductor containing numerous charged dislocations is considered. It is assumed that there is a constant electric field that creates an electric current. The situation is similar to the case of the propagation of ultrasonic waves in piezoelectric semiconductors, but in the problem under consideration, instead of the electric field due to the piezoelectric properties of the medium, the electric field of dislocations appears