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Liquid metals (LM) are embedded in an elastomer matrix to obtain soft composites with unique thermal, dielectric, and mechanical properties. They have applications in soft robotics, biomedical engineering, and wearable electronics. By linking the structure to the properties of these materials, it is possible to perform material design rationally. Liquid-metal embedded elastomers (LMEEs) have been designed for targeted electro-thermo-mechanical properties by semi-supervised learning of structure-property (SP) links in a variational autoencoder network (VAE). The design parameters are the microstructural descriptors that are physically meaningful and have affine relationships with the synthetization of the studied particulate composite. The machine learning (ML) model is trained on a generated dataset of microstructural descriptors with their multifunctional property quantities as their labels. Sobol sequence is used for in-silico Design of Experiment (DoE) by sampling the design space to generate a comprehensive dataset of 3D microstructure realizations via a packing algorithm. The mechanical responses of the generated microstructures are simulated using a previously developed Finite Element (FE) model, considering the surface tension induced by LM inclusions, while the linear thermal and dielectric constants are homogenized with the help of our in-house Fast Fourier Transform (FFT) package. Following the training by minimization of an appropriate loss function, the VAE encoder acts as the surrogate of numerical solvers of the multifunctional homogenizations, and its decoder is used for the material design. Our results indicate the satisfactory performance of the surrogate model and the inverse calculator with respect to high-fidelity numerical simulations validated with LMEE experimental results.