Related papers: Differential Euler: Designing a Neural Network app…
With the explosive growth of available training data, single-image 3D human modeling is ahead of a transition to a data-centric paradigm. A key to successfully exploiting data scale is to design flexible models that can be supervised from…
We propose Trusted Neural Network (TNN) models, which are deep neural network models that satisfy safety constraints critical to the application domain. We investigate different mechanisms for incorporating rule-based knowledge in the form…
The three-body problem is arguably the oldest open question in astrophysics, and has resisted a general analytic solution for centuries. Various implementations of perturbation theory provide solutions in portions of parameter space, but…
For light nuclei, ab initio many-body methods such as the no-core shell model are the tools of choice for predictive, high-precision nuclear structure calculations. The applicability and the level of precision of these methods, however, is…
Deep learning has been extended to a number of new domains with critical success, though some traditional orienteering problems such as the Travelling Salesman Problem (TSP) and its variants are not commonly solved using such techniques.…
A novel artificial neural network method is proposed for solving Cauchy inverse problems. It allows multiple hidden layers with arbitrary width and depth, which theoretically yields better approximations to the inverse problems. In this…
Neural operators are a type of deep architecture that learns to solve (i.e. learns the nonlinear solution operator of) partial differential equations (PDEs). The current state of the art for these models does not provide explicit…
Humans effortlessly infer the 3D shape of objects. What computations underlie this ability? Although various computational models have been proposed, none of them capture the human ability to match object shape across viewpoints. Here, we…
We discuss the general three-particle quantum scattering problem, for motion restricted to the full line. Specifically, we formulate the three-body problem in one dimension in terms of the (Faddeev-type) integral equation approach. As a…
The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are…
Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…
A unified approach, for solving a wide class of single and many-body quantum problems, commonly encountered in literature is developed based on a recently proposed method for finding solutions of linear differential equations. Apart from…
Motivated by experimental probes of general relativity, we adopt methods from perturbative (quantum) field theory to compute, up to certain integrals, the effective lagrangian for its n-body problem. Perturbation theory is performed about a…
We present a formalism for constructing schematic diagrams to depict chaotic three-body interactions in Newtonian gravity. This is done by decomposing each interaction in to a series of discrete transformations in energy- and angular…
Inertial measurement units are commonly used to estimate the attitude of moving objects. Numerous nonlinear filter approaches have been proposed for solving the inherent sensor fusion problem. However, when a large range of different…
The estimation of 3D human body shape and clothing measurements is crucial for virtual try-on and size recommendation problems in the fashion industry but has always been a challenging problem due to several conditions, such as lack of…
A long-standing goal of nuclear theory is to explain how the structure and dynamics of atomic nuclei and neutron-star matter emerge from the underlying interactions among protons and neutrons. Achieving this goal requires solving the…
This paper introduces the first deep neural network-based estimation metric for the jigsaw puzzle problem. Given two puzzle piece edges, the neural network predicts whether or not they should be adjacent in the correct assembly of the…
Neural networks have been identified as powerful tools for the study of complex systems. A noteworthy example is the neural network differential equation (NN DE) solver, which can provide functional approximations to the solutions of a wide…
There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine…