Differentiable neural network representation of multi-well, locally-convex potentials | Paper Citation Record

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This paper cites Classical dynamics of a coupled double well oscillator in condensed mediaa.

Differentiable neural network representation of multi-well, locally-convex potentials Classical dynamics of a coupled double well oscillator in condensed mediaa

Reference 1

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This paper cites Relaxation of classical particles in anharmonic multi- well potentials.

Differentiable neural network representation of multi-well, locally-convex potentials Relaxation of classical particles in anharmonic multi- well potentials

Reference 2

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This paper cites Double wells.

Differentiable neural network representation of multi-well, locally-convex potentials Double wells

Reference 3

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This paper cites Multi-well potentials in quantum mechanics and stochastic processes.

Differentiable neural network representation of multi-well, locally-convex potentials Multi-well potentials in quantum mechanics and stochastic processes

Reference 4

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This paper cites The double-well potential in quantum mechanics: a simple, numerically exact formula- tion.

Differentiable neural network representation of multi-well, locally-convex potentials The double-well potential in quantum mechanics: a simple, numerically exact formula- tion

Reference 5

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This paper cites The development of transition-state theory.

Differentiable neural network representation of multi-well, locally-convex potentials The development of transition-state theory

Reference 6

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This paper cites Current status of transition-state theory.

Differentiable neural network representation of multi-well, locally-convex potentials Current status of transition-state theory

Reference 7

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This paper cites Nonlocal phase transitions in homogeneous and periodic media.

Differentiable neural network representation of multi-well, locally-convex potentials Nonlocal phase transitions in homogeneous and periodic media

Reference 8

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This paper cites Double-well potentials and structural phase transitions in polyphenyls.

Differentiable neural network representation of multi-well, locally-convex potentials Double-well potentials and structural phase transitions in polyphenyls

Reference 9

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This paper cites On the limit behavior of lattice-type metamaterials with bi-stable mechanisms.

Differentiable neural network representation of multi-well, locally-convex potentials On the limit behavior of lattice-type metamaterials with bi-stable mechanisms

Reference 10

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This paper cites Stacking for non-mixing bayesian computations: The curse and blessing of multimodal posteriors.

Differentiable neural network representation of multi-well, locally-convex potentials Stacking for non-mixing bayesian computations: The curse and blessing of multimodal posteriors

Reference 11

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This paper cites Multimodal estimation of distribution algorithms.

Differentiable neural network representation of multi-well, locally-convex potentials Multimodal estimation of distribution algorithms

Reference 12

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This paper cites Generalized Multimodal ELBO.

Differentiable neural network representation of multi-well, locally-convex potentials Generalized Multimodal ELBO

Reference 13

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This paper cites The relaxation of a double-well energy.

Differentiable neural network representation of multi-well, locally-convex potentials The relaxation of a double-well energy

Reference 14

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Observation 046faa4a-56b5-4d05-aadf-a3d6bc731cbf · outbound

This paper cites Geometric parameters and the relaxation of multiwell energies.

Differentiable neural network representation of multi-well, locally-convex potentials Geometric parameters and the relaxation of multiwell energies

Reference 15

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This paper cites Solid–solid phase transition modelling.

Differentiable neural network representation of multi-well, locally-convex potentials Solid–solid phase transition modelling

Reference 16

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Observation 5381ea17-9257-4dbd-8c07-ef14989b9b9a · outbound

This paper cites On the relation of a three-well energy.

Differentiable neural network representation of multi-well, locally-convex potentials On the relation of a three-well energy

Reference 17

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This paper cites Statistical Mechanics.

Differentiable neural network representation of multi-well, locally-convex potentials Statistical Mechanics

Reference 18

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This paper cites Pattern recognition and machine learning, volume 4.

Differentiable neural network representation of multi-well, locally-convex potentials Pattern recognition and machine learning, volume 4

Reference 19

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This paper cites On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning.

Differentiable neural network representation of multi-well, locally-convex potentials On the Properties of the Softmax Function with Application in Game Theory and Reinforcement Learning

Reference 20

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This paper cites Accurately computing the log-sum-exp and softmax functions.

Differentiable neural network representation of multi-well, locally-convex potentials Accurately computing the log-sum-exp and softmax functions

Reference 21

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Observation 6687d13c-3407-4b76-8591-c50a8a8af461 · outbound

This paper cites Convex optimization.

Differentiable neural network representation of multi-well, locally-convex potentials Convex optimization

Reference 22

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This paper cites Smoothing and first order methods: A unified framework.

Differentiable neural network representation of multi-well, locally-convex potentials Smoothing and first order methods: A unified framework

Reference 23

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This paper cites Smoothing method for minimax problems.

Differentiable neural network representation of multi-well, locally-convex potentials Smoothing method for minimax problems

Reference 24

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This paper cites Smooth minimization of non-smooth functions.

Differentiable neural network representation of multi-well, locally-convex potentials Smooth minimization of non-smooth functions

Reference 25

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Observation c82ceafd-fa56-472c-8db8-7f5671b4fc9c · outbound

This paper cites Variational models for microstructure and phase transitions.

Differentiable neural network representation of multi-well, locally-convex potentials Variational models for microstructure and phase transitions

Reference 26

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This paper cites Input convex neural networks.

Differentiable neural network representation of multi-well, locally-convex potentials Input convex neural networks

Reference 27

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Observation 4d97a9cb-c843-42f9-a22c-1889f19f6e21 · outbound

This paper cites Data-driven tissue mechanics with polyconvex neural ordinary differential equations.

Differentiable neural network representation of multi-well, locally-convex potentials Data-driven tissue mechanics with polyconvex neural ordinary differential equations

Reference 28

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Observation 8c3d6565-03d0-4bbb-9f43-b97e83933cd1 · outbound

This paper cites Polyconvex neural networks for hyperelastic constitutive models: A rectifi- cation approach.

Differentiable neural network representation of multi-well, locally-convex potentials Polyconvex neural networks for hyperelastic constitutive models: A rectifi- cation approach

Reference 29

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Observation 9ec03dc1-f9f4-4f2f-b28e-683f397bfa9a · outbound

This paper cites A mechanics-informed artificial neural network approach in data- driven constitutive modeling.

Differentiable neural network representation of multi-well, locally-convex potentials A mechanics-informed artificial neural network approach in data- driven constitutive modeling

Reference 30

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This paper cites Learning constitutive relations using symmetric positive definite neural networks.

Differentiable neural network representation of multi-well, locally-convex potentials Learning constitutive relations using symmetric positive definite neural networks

Reference 31

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This paper cites Polyconvex anisotropic hyperelasticity with neural networks.

Differentiable neural network representation of multi-well, locally-convex potentials Polyconvex anisotropic hyperelasticity with neural networks

Reference 32

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This paper cites Parametrized polyconvex hyperelasticity with physics-augmented neural networks.

Differentiable neural network representation of multi-well, locally-convex potentials Parametrized polyconvex hyperelasticity with physics-augmented neural networks

Reference 33

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This paper cites Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria.

Differentiable neural network representation of multi-well, locally-convex potentials Neural network-based multiscale modeling of finite strain magneto-elasticity with relaxed convexity criteria

Reference 34

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This paper cites Learning hyperelastic anisotropy from data via a tensor basis neural network.

Differentiable neural network representation of multi-well, locally-convex potentials Learning hyperelastic anisotropy from data via a tensor basis neural network

Reference 35

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This paper cites Polyconvex neural network models of thermoelasticity.

Differentiable neural network representation of multi-well, locally-convex potentials Polyconvex neural network models of thermoelasticity

Reference 36

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This paper cites Automated model discovery of finite strain elastoplasticity from uniaxial experiments.

Differentiable neural network representation of multi-well, locally-convex potentials Automated model discovery of finite strain elastoplasticity from uniaxial experiments

Reference 37

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Observation d6f8d809-1821-4bff-8e15-6613c17ea640 · outbound

This paper cites Optimal transport mapping via input convex neural networks.

Differentiable neural network representation of multi-well, locally-convex potentials Optimal transport mapping via input convex neural networks

Reference 38

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This paper cites Optimal Control Via Neural Networks: A Convex Approach.

Differentiable neural network representation of multi-well, locally-convex potentials Optimal Control Via Neural Networks: A Convex Approach

Reference 39

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This paper cites On physics-informed data-driven isotropic and anisotropic constitutive mod- els through probabilistic machine learning and space-filling sampling.

Differentiable neural network representation of multi-well, locally-convex potentials On physics-informed data-driven isotropic and anisotropic constitutive mod- els through probabilistic machine learning and space-filling sampling

Reference 40

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Observation 6bfd2d50-88aa-47de-9838-735d50e45e79 · outbound

This paper cites Cdinn–convex difference neural networks.

Differentiable neural network representation of multi-well, locally-convex potentials Cdinn–convex difference neural networks

Reference 41

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Observation ec06fe6f-2e9f-4a42-8df2-b25265012d66 · outbound

This paper cites Input Specific Neural Networks.

Differentiable neural network representation of multi-well, locally-convex potentials Input Specific Neural Networks

Reference 42

Resolution: verified exact; local_arxiv, observed 2026-08-07T10:19:14.064105Z

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Observation 73d900ad-4c92-4165-942f-07f5dbcf7d8b · outbound

This paper cites Convexity conditions and existence theorems in nonlinear elasticity.Archive for rational mechanics and Analysis, 63:337–403, 1976.

Differentiable neural network representation of multi-well, locally-convex potentials Convexity conditions and existence theorems in nonlinear elasticity.Archive for rational mechanics and Analysis, 63:337–403, 1976

Reference 43

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:19.151128Z

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Observation d7a0c765-716c-4e61-bdaa-e981d58d4f7d · outbound

This paper cites Loss of polyconvexity by homogenization.

Differentiable neural network representation of multi-well, locally-convex potentials Loss of polyconvexity by homogenization

Reference 44

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Observation 3f1e7335-0ac9-4ba0-8141-c1a1aeeedc77 · outbound

This paper cites An assessment of numerical techniques to find energy-minimizing microstructures associated with nonconvex potentials.

Differentiable neural network representation of multi-well, locally-convex potentials An assessment of numerical techniques to find energy-minimizing microstructures associated with nonconvex potentials

Reference 45

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:18.921763Z

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Observation bc90c6de-d4ff-4472-9c40-4829a090f180 · outbound

This paper cites Experiment-informed finite-strain inverse design of spinodal metamaterials.

Differentiable neural network representation of multi-well, locally-convex potentials Experiment-informed finite-strain inverse design of spinodal metamaterials

Reference 46

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This paper cites Discovering governing equation from data for multi-stable energy harvester under white noise.

Differentiable neural network representation of multi-well, locally-convex potentials Discovering governing equation from data for multi-stable energy harvester under white noise

Reference 47

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Observation 225e00f3-4e77-4b28-a664-63a4f98d03b6 · outbound

This paper cites An attention-based neural ordinary differential equation framework for modeling inelastic processes.

Differentiable neural network representation of multi-well, locally-convex potentials An attention-based neural ordinary differential equation framework for modeling inelastic processes

Reference 48

Resolution: verified exact; local_arxiv, observed 2026-08-07T10:19:13.784975Z

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Observation 65f5631a-75d1-4028-aa33-69faf194f4ba · outbound

This paper cites Density-preserving hierarchical em algorithm: Simplifying gaussian mixture models for approximate inference.

Differentiable neural network representation of multi-well, locally-convex potentials Density-preserving hierarchical em algorithm: Simplifying gaussian mixture models for approximate inference

Reference 49

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:18.555124Z

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Observation 2be2bc95-1e36-40fb-9a1d-4d363240a603 · outbound

This paper cites Melm-grbf: A modified version of the extreme learning machine for generalized radial basis function neural networks.

Differentiable neural network representation of multi-well, locally-convex potentials Melm-grbf: A modified version of the extreme learning machine for generalized radial basis function neural networks

Reference 50

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:18.449454Z

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Observation 69cbf5b6-c48a-44c7-a179-0733146df54f · outbound

This paper cites Primal-gmm: Parametric manifold learning of gaussian mixture models.

Differentiable neural network representation of multi-well, locally-convex potentials Primal-gmm: Parametric manifold learning of gaussian mixture models

Reference 51

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:18.327148Z

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Observation f1187365-2afe-4d4f-ae0b-2ee72dd6fb9d · outbound

This paper cites Sparse regression.

Differentiable neural network representation of multi-well, locally-convex potentials Sparse regression

Reference 52

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:18.127247Z

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Observation 65734a19-1084-40ef-b0fc-9f056a59fe24 · outbound

This paper cites Adam: A method for stochastic optimization.

Differentiable neural network representation of multi-well, locally-convex potentials Adam: A method for stochastic optimization

Reference 53

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This paper cites Perspectives on the mathematics of biological patterning and morphogenesis.

Differentiable neural network representation of multi-well, locally-convex potentials Perspectives on the mathematics of biological patterning and morphogenesis

Reference 54

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:17.814907Z

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Observation 7385b28d-0c46-4786-b267-8a33c1998eff · outbound

This paper cites Mechanochemical spinodal decomposition: a phenomenological theory of phase transformations in multi-component, crystalline solids.

Differentiable neural network representation of multi-well, locally-convex potentials Mechanochemical spinodal decomposition: a phenomenological theory of phase transformations in multi-component, crystalline solids

Reference 55

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:17.457293Z

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This paper cites Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order disorder transitions in LixCoO2.

Differentiable neural network representation of multi-well, locally-convex potentials Bridging scales with Machine Learning: From first principles statistical mechanics to continuum phase field computations to study order disorder transitions in LixCoO2

Reference 56

Resolution: verified exact; local_arxiv, observed 2026-08-07T10:19:13.484554Z

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Observation 5ce0ca63-6fb4-4044-92de-4bf8f11ae494 · outbound

This paper cites Chemical reaction models for non-equilibrium phase transitions.

Differentiable neural network representation of multi-well, locally-convex potentials Chemical reaction models for non-equilibrium phase transitions

Reference 57

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:17.085687Z

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This paper cites Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the schl ¨ogl model revisited.

Differentiable neural network representation of multi-well, locally-convex potentials Stochastic dynamics and non-equilibrium thermodynamics of a bistable chemical system: the schl ¨ogl model revisited

Reference 58

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:16.689073Z

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Observation 6cdfe37b-5152-4900-b74c-04cd2aa38b39 · outbound

This paper cites Exact stochastic simulation of coupled chemical reactions.

Differentiable neural network representation of multi-well, locally-convex potentials Exact stochastic simulation of coupled chemical reactions

Reference 59

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:16.317181Z

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Observation 637202f2-0267-4ef5-a0a5-2932d228d1e3 · outbound

This paper cites Stochastic simulation of chemical kinetics.

Differentiable neural network representation of multi-well, locally-convex potentials Stochastic simulation of chemical kinetics

Reference 60

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:16.025625Z

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Observation 49d6cf57-c44b-41b9-977e-3faefdf3032a · outbound

This paper cites Spectral representation and reduced order modeling of the dynamics of stochastic reaction networks via adaptive data partitioning.

Differentiable neural network representation of multi-well, locally-convex potentials Spectral representation and reduced order modeling of the dynamics of stochastic reaction networks via adaptive data partitioning

Reference 61

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:15.661354Z

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Observation 3b27e497-742e-4f66-912f-33ebfb448de8 · outbound

This paper cites Uncertainty quantification of neural network models of evolving processes via Langevin sampling.

Differentiable neural network representation of multi-well, locally-convex potentials Uncertainty quantification of neural network models of evolving processes via Langevin sampling

Reference 62

Resolution: verified exact; local_arxiv, observed 2026-08-07T10:19:13.205144Z

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Observation 4c1f98d7-7953-4f19-b6ec-8c4d035e4d1d · outbound

This paper cites Variational inference: A review for statisticians.

Differentiable neural network representation of multi-well, locally-convex potentials Variational inference: A review for statisticians

Reference 63

Resolution: unresolved; no resolver link, observed 2026-08-07T10:19:12.219061Z

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Observation 31ace67f-16ec-4db4-99ad-05a1c6004586 · outbound

This paper cites A neural ordinary differential equation framework for modeling inelastic stress response via internal state variables.

Differentiable neural network representation of multi-well, locally-convex potentials A neural ordinary differential equation framework for modeling inelastic stress response via internal state variables

Reference 64

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:15.289776Z

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Observation c8de2496-6a91-48f7-9a14-0089decd3230 · outbound

This paper cites The epigenetic landscape in the course of time: Conrad hal waddington’s methodological impact on the life sciences.

Differentiable neural network representation of multi-well, locally-convex potentials The epigenetic landscape in the course of time: Conrad hal waddington’s methodological impact on the life sciences

Reference 65

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:14.951155Z

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Observation 227a750c-aee5-4a40-b082-95884230d4ed · outbound

This paper cites Quantifying the waddington landscape and biological paths for development and differentiation.

Differentiable neural network representation of multi-well, locally-convex potentials Quantifying the waddington landscape and biological paths for development and differentiation

Reference 66

Resolution: unresolved; no resolver link, observed 2026-08-07T10:19:12.573942Z

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Observation 3d9b92a6-d204-441b-b468-1500e8adbb0f · outbound

This paper cites Sur les mat ´eriaux standard g ´en´eralis´es.

Differentiable neural network representation of multi-well, locally-convex potentials Sur les mat ´eriaux standard g ´en´eralis´es

Reference 67

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:14.681425Z

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Observation cafc8175-97c2-404f-8081-8345e3daaf73 · outbound

This paper cites The derivation of constitutive relations from the free energy and the dissipa- tion function.

Differentiable neural network representation of multi-well, locally-convex potentials The derivation of constitutive relations from the free energy and the dissipa- tion function

Reference 68

Resolution: verified fuzzy; raw_fallback, observed 2026-08-07T10:19:14.354256Z

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