  Many mobile sensing applications utilize data from various modalities,
including motion and physiological sensors in mobile and wearable devices.
Federated Learning (FL) is particularly suitable for these applications thanks
to its privacy-preserving feature. However, challenges such as limited battery
life, poor network conditions, and sensor malfunctions can restrict the use of
all available modalities for local model training. Additionally, existing
multimodal FL systems also struggle with scalability and efficiency as the
number of modality sources increases. To address these issues, we introduce
FLISM, a framework designed to enable multimodal FL with incomplete modalities.
FLISM leverages simulation technique to learn robust representations that can
handle missing modalities and transfers model knowledge across clients with
varying set of modalities. The evaluation results using three real-world
datasets and simulations demonstrate FLISM's effective balance between model
performance and system efficiency. It shows an average improvement of .067 in
F1-score, while also reducing communication (2.69x faster) and computational
(2.28x more efficient) overheads compared to existing methods addressing
incomplete modalities. Moreover, in simulated scenarios involving tasks with a
larger number of modalities, FLISM achieves a significant speedup of
3.23x~85.10x in communication and 3.73x~32.29x in computational efficiency.
