The battery enclosures of current electric vehicles are made of metallic alloys, specifically aluminum or steel. Replacing these metallic alloys with a lightweight material, such as carbon fiber composite, may offer significant weight savings due to its comparable strength-to-weight ratio. Carbon fiber is corrosion-resistant and can be engineered for fire resistance and electrical insulation. It can also be fine-tuned for specific applications and performance needs, such as "crashworthiness".Designing a carbon fiber-based battery enclosure for crash performance through trial-and-error experiments can be extremely laborious and inefficient. This inefficiency can be alleviated by using virtual manufacturing and structural analysis software. A simulation software chain allows for the virtual manufacturing and crash-testing of the battery enclosure in a single process. However, these numerical simulations are computationally expensive, time-consuming, and may require significant user interaction. Finding optimal design parameters within a reasonable time-frame can be extremely challenging.The first part of this dissertation addresses the forward problem of accelerating the design of battery enclosures for crash performance. It involves developing a machine learning-based surrogate model of the simulation workflow that can provide quick, approximate results in a fraction of seconds. This can further support design space exploration studies.Physical phenomena in engineering design are governed by differential equations, typically solved in a forward manner with known physical parameters, initial and/or boundary conditions, and a source term. However, there is often a need to reconstruct the source term from available measurement data, which may be corrupted with noise, along with the initial and/or boundary conditions, and physical parameters. These types of problems are known as inverse problems, more specifically, inverse source problems. Inverse source problems are often ill-posed and are usually solved by iterative schemes and optimization techniques with regularization, which can be time-consuming. In recent years, machine learning approaches have shown promise in managing ill-posed problems and handling noisy data.The second part of this dissertation addresses a specific type of inverse source problem, known as the dynamic load identification problem, which involves determining the time-varying forces acting on a mechanical system from the sensor measurements. The study begins with the development of a deep learning model that leverages physics information to infer the forcing functions of both linear and nonlinear oscillators from observational data. Furthermore, the study leads up to a development of a physically consistent surrogate model that is capable of providing robust predictions from the noisy observations without the need to explicitly solve the differential equation.