Abstract
In recent years, the field of neural fields has seen a significant surge in interest, particularly following the introduction of Neural Radiance Fields (NeRFs), which benefitted from the advancements in sinusoidal activation functions. This new implicit representation, offered by neural fields, facilitates a detailed and continuous representation of complex data through a compact and flexible neural network model, efficiently learned from sparse and irregular data samples. Concurrently, there has been an increasing focus on Physics-Informed Neural Networks (PINNs), which are gaining traction across various computational domains. PINNs integrate physical law with machine learning models, thereby improving both accuracy and interpretability in simulating and predicting complex phenomena. The synergy between neural fields and PINNs has introduced a new,
powerful approach to solving inversion problems. Early works have started to explore this direction for applications like topology optimization and gravity inversion.
In this presentation, we explore the use of neural fields for inversion problems. We focus on source inversion problems, where sparse measurements are used for inferring the source of some given physical process, such as heat source locations in thermal analysis, determining the epicentre of an earthquake, and identifying the main sources of acoustic noise in a region. We demonstrate the use of physics-informed neural fields in heat conduction, to estimate the location and intensity of heat sources under constrained conditions. Moreover, we highlight the potential of neural fields in addressing highly nonlinear challenges and their implications in solving ill-posed problems. This methodology presents a practical and efficient solution for real-world scenarios characterised by complex interactions and limited data availability. Our presentation highlights the potential of neural fields in
addressing diverse inversion problems across multiple applications. We believe that this approach will become a key computational method in the field, offering novel and effective solutions for complex challenges.
powerful approach to solving inversion problems. Early works have started to explore this direction for applications like topology optimization and gravity inversion.
In this presentation, we explore the use of neural fields for inversion problems. We focus on source inversion problems, where sparse measurements are used for inferring the source of some given physical process, such as heat source locations in thermal analysis, determining the epicentre of an earthquake, and identifying the main sources of acoustic noise in a region. We demonstrate the use of physics-informed neural fields in heat conduction, to estimate the location and intensity of heat sources under constrained conditions. Moreover, we highlight the potential of neural fields in addressing highly nonlinear challenges and their implications in solving ill-posed problems. This methodology presents a practical and efficient solution for real-world scenarios characterised by complex interactions and limited data availability. Our presentation highlights the potential of neural fields in
addressing diverse inversion problems across multiple applications. We believe that this approach will become a key computational method in the field, offering novel and effective solutions for complex challenges.
