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Image animation has become a promising area in multimodal research, with a focus on generating videos from reference images. While prior work has largely emphasized generic video generation guided by text, music-driven dance video generation remains underexplored. In this paper, we introduce MuseDance, an innovative end-to-end model that animates reference images using both music and text inputs. This dual input enables MuseDance to generate personalized videos that follow text descriptions and synchronize character movements with the music. Unlike existing approaches, MuseDance eliminates the need for complex motion guidance inputs, such as pose or depth sequences, making flexible and creative video generation accessible to users of all expertise levels. To advance research in this field, we present a new multimodal dataset comprising 2,904 dance videos with corresponding background music and text descriptions. Our approach leverages diffusion-based methods to achieve robust generalization, precise control, and temporal consistency, setting a new baseline for the music-driven image animation task.

We provide a new non-invasive, easy-to-scale for large amounts of subjects and a remotely accessible method for (hidden) emotion detection from videos of human faces. Our approach combines face manifold detection for accurate location of the face in the video with local face manifold embedding to create a common domain for the measurements of muscle micro-movements that is invariant to the movement of the subject in the video. In the next step, we employ the Digital Image Speckle Correlation (DISC) and the optical flow algorithm to compute the pattern of micro-movements in the face. The corresponding vector field is mapped back to the original space and superimposed on the original frames of the videos. Hence, the resulting videos include additional information about the direction of the movement of the muscles in the face. We take the publicly available CK++ dataset of visible emotions and add to it videos of the same format but with hidden emotions. We process all the videos using our micro-movement detection and use the results to train a state-of-the-art network for emotions classification from videos -- Frame Attention Network (FAN). Although the original FAN model achieves very high out-of-sample performance on the original CK++ videos, it does not perform so well on hidden emotions videos. The performance improves significantly when the model is trained and tested on videos with the vector fields of muscle movements. Intuitively, the corresponding arrows serve as edges in the image that are easily captured by the convolutions filters in the FAN network.

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal approximators capable of estimating the solution of any physical law described by a system of PDEs, which serves as a regularization during neural network training, restricting the space of admissible solutions and enhancing function approximation accuracy. We demonstrate that when the system exhibits sudden changes in the PDE dynamics, this regularization is either insufficient to accurately estimate the true dynamics, or it may result in model miscalibration and failure. Consequently, we propose a PINNs extension using a Total-Variation penalty, which allows to accommodate multiple changepoints in the PDE dynamics and significantly improves function approximation. These changepoints can occur at random locations over time and are estimated concurrently with the solutions. Additionally, we introduce an online learning method for re-weighting loss function terms dynamically. Through empirical analysis using examples of various equations with parameter changes, we showcase the advantages of our proposed model. In the absence of changepoints, the model reverts to the original PINNs model. However, when changepoints are present, our approach yields superior parameter estimation, improved model fitting, and reduced training error compared to the original PINNs model.