**5. Concluding Remarks**

A physics-informed neural network (PINN) applicable to solve initial and boundary value problems has been established. The PINN was applied to solve an initial value problem described by a first order ordinary differential equation and to solve the Reynolds boundary value problem, described by a second order ordinary differential equation. Both these problems were selected since they can be solved analytically, and the error analysis showed that the predictions returned by the PINN was in good agreement with the analytical solutions for the specifications given. The advantage of the present approach is, however, neither accuracy nor efficiency when solving these linear equations, but that it presents a meshless method and that it is not data driven. This concept may, of course, be generalised, and it is hypothesised that future research in this direction may lead to more accurate and efficient in solving related but nonlinear problems than currently available routines.

**Funding:** The author acknowledges support from VR (The Swedish Research Council): DNR 2019- 04293.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** Not applicable.

**Conflicts of Interest:** The author declares no conflict of interest.

#### **References**

