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Related Concept Videos

Three-Dimensional Force System:Problem Solving01:30

Three-Dimensional Force System:Problem Solving

A three-dimensional force system refers to a scenario in which three forces act simultaneously in three different directions. This type of problem is commonly encountered in physics and engineering, where it is necessary to calculate the resultant force on the system, which can then be used to predict or analyze the behavior of the object or structure under consideration.
To solve a three-dimensional force system, first resolve each force into its respective scalar components. Do this using...
Three-Dimensional Force System01:30

Three-Dimensional Force System

In mechanical engineering, a three-dimensional force system is a system of forces acting in three dimensions, with forces applied along the x, y, and z coordinate axes. The three-dimensional force system is an important concept in mechanical engineering, as it allows engineers to understand and analyze the behavior of objects and structures in three dimensions. By understanding the forces acting on a system, engineers can design more efficient and effective mechanical systems that can withstand...
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Depth Perception and Spatial Vision

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The Principle of Superposition and the Gravitational Field01:17

The Principle of Superposition and the Gravitational Field

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Related Experiment Video

Updated: Jun 6, 2026

3D-Neuronavigation In Vivo Through a Patient's Brain During a Spontaneous Migraine Headache
10:39

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Published on: June 2, 2014

Three-dimensional inversion of gravity data using implicit neural representations and scientific machine learning.

Pankaj K Mishra1, Sanni Laaksonen2, Jochen Kamm2

  • 1Geological Survey of Finland, Vuorimiehentie 5, Espoo, Finland. pankaj.mishra@gtk.fi.

Scientific Reports
|June 4, 2026
PubMed
Summary

We developed a new machine learning method for 3D gravity inversion using implicit neural representations (INRs). This approach accurately maps subsurface density variations for resource exploration and geological studies.

Keywords:
GravityInversionNeural fieldsPhysics-based deep learningScientific machine learning

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Last Updated: Jun 6, 2026

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Published on: June 2, 2014

Area of Science:

  • Geophysics
  • Machine Learning
  • Computational Science

Background:

  • Gravity inversion is crucial for understanding subsurface density variations.
  • Applications include mineral exploration, geothermal energy, carbon storage, and groundwater management.
  • Current methods often rely on mesh-based discretizations, which can limit scalability and flexibility.

Purpose of the Study:

  • To present a novel scientific machine learning approach for 3D gravity inversion.
  • To represent subsurface density as a continuous field using implicit neural representations (INRs).
  • To overcome limitations of traditional mesh-based methods.

Main Methods:

  • Utilized a deep neural network trained via a physics-based forward-model loss.
  • Employed spatial encoding to improve the capture of sharp density contrasts and short-wavelength features.
  • Applied the method to synthetic datasets, including complex geological models and dipping block structures.

Main Results:

  • The INR framework successfully reconstructed detailed subsurface structures and geologically plausible boundaries.
  • Achieved accurate inversion without explicit regularization or depth weighting.
  • Demonstrated reduced inversion parameters with increasing problem size, indicating scalability.

Conclusions:

  • Implicit neural representations offer a scalable, flexible, and interpretable framework for large-scale geophysical inversion.
  • This approach shows significant potential for advancing gravity inversion techniques.
  • The framework is adaptable for other geophysical methods and joint/multiphysics inversions.