Fungal wood decay is a complex biophysical phenomenon that involves the degradation of a variety of structural wood components, ranging from lignin and carbohydrates to defensive chemical agents. All these substrates serve as varying resources with different material properties that determine the rate of fungal propagation and the structural integrity and color of decaying wood. We propose a novel approach to simulate the dynamic interactions between the biological and mechanical components of wood decay, including fungal colonization, chemical defense, and moisture-driven fracture. We propose a novel volumetric representation of trees that includes grain-aligned mesh generation, internal moisture dynamics, and tissue-specific health states. Furthermore, we model the anisotropic diffusion, consumption, and resulting material failure caused by white and brown rot fungi. This allows simulating and rendering 3D volumetric decaying trees that realistically capture key aspects of the process, such as the progression of cuboid fracture patterns, the hollowing of trunks, and the effects of environmental moisture on structural stability.

Neural shape representation generally refers to representing 3D geometry using neural networks, e.g., computing a signed distance or occupancy value at a specific spatial position. In this paper we present a neural-network architecture suitable for accurate encoding of 3D shapes in a single forward pass. Our architecture is based on a multi-scale hybrid system incorporating graph-based and voxel-based components, as well as a continuously differentiable decoder. The hybrid system includes a novel way of voxelizing point-based features in neural networks by projecting the point "feature-field" onto a grid. This projection is insensitive to local point density, and we show that it can be used to obtain smoother and more detailed reconstructions, in particular when combined with oriented point clouds as input. Our architecture also requires only a single forward pass, instead of the latent-code optimization used in auto-decoder methods. Furthermore, our network is trained to solve the well-established eikonal equation and only requires knowledge of the zero-level set for training and inference. We additionally propose a modification to the aforementioned loss function for the case that surface normals are not well defined, e.g., in the context of non-watertight surfaces and non-manifold geometry. Overall, our method consistently outperforms other baselines on the surface reconstruction task across a wide variety of datasets, while being more computationally efficient and requiring fewer parameters.

We present Perm, a learned parametric representation of human 3D hair designed to facilitate various hair-related applications. Unlike previous work that jointly models the global hair structure and local curl patterns, we propose to disentangle them using a PCA-based strand representation in the frequency domain, thereby allowing more precise editing and output control. Specifically, we leverage our strand representation to fit and decompose hair geometry textures into low- to high-frequency hair structures, termed guide textures and residual textures, respectively. These decomposed textures are later parameterized with different generative models, emulating common stages in the hair grooming process. We conduct extensive experiments to validate the architecture design of Perm, and finally deploy the trained model as a generic prior to solve task-agnostic problems, further showcasing its flexibility and superiority in tasks such as single-view hair reconstruction, hairstyle editing, and hair-conditioned image generation. More details can be found on our project page: https://cs.yale.edu/homes/che/projects/perm/.

We propose a transformer architecture and training strategy for tree generation. The architecture processes data at multiple resolutions and has an hourglass shape, with middle layers processing fewer tokens than outer layers. Similar to convolutional networks, we introduce longer-range skip connections to complement this multi-resolution approach. The key advantages of this architecture are the faster processing speed and lower memory consumption. We are, therefore, able to process more complex trees than would be possible with a vanilla transformer architecture. Furthermore, we extend this approach to perform image-to-tree and point-cloud-to-tree conditional generation and to simulate the tree growth processes, generating 4D trees. Empirical results validate our approach in terms of speed, memory consumption, and generation quality.

We present a novel combustion simulation framework to model fire phenomena across solids, liquids, and gases. Our approach extends traditional fluid solvers by incorporating multi-species thermodynamics and reactive transport for fuel, oxygen, nitrogen, carbon dioxide, water vapor, and residuals. Combustion reactions are governed by stoichiometry-dependent heat release, allowing an accurate simulation of premixed and diffusive flames with varying intensity and composition. We support a wide range of scenarios including jet fires, water suppression (sprays and sprinklers), fuel evaporation, and starvation conditions. Our framework enables interactive heat sources, fire detectors, and realistic rendering of flames (e.g., laminar-to-turbulent transitions and blue-to-orange color shifts). Our key contributions include the tight coupling of species dynamics with thermodynamic feedback, evaporation modeling, and a hybrid SPH-grid representation for the efficient simulation of extinguishing fires. We validate our method through numerous experiments that demonstrate its versatility in both indoor and outdoor fire scenarios.

Thunderstorms are complex multiphysics phenomena driven by charge transfer processes arising from interactions between ice and water particles in the atmosphere. We present a physically grounded model for simulating cloud electrification and lightning discharge, capable of generating diverse lightning types as emergent responses to evolving atmospheric conditions. Our approach requires only a minimal set of atmospheric parameters and no user-defined triggers. Charge separation is modeled at the microphysical level using a statistical mechanics framework, while discharges are captured through a novel gauge-invariant dielectric breakdown model that accounts for bipolar channels, dynamic electric fields, and air resistance. We validate our method through comparisons with observational data and prior models, demonstrating its ability to simulate distinct discharge types and the full life cycle of thunderstorms. Beyond scientific accuracy, our framework supports real-time nowcasting, civil engineering assessments, virtual environment generation, and the simulation of complex dielectric breakdown in varied contexts.

Cyclones are large-scale phenomena that result from complex heat and water transfer processes in the atmosphere, as well as from the interaction of multiple hydrometeors , i.e., water and ice particles. When cyclones make landfall, they are considered natural disasters and spawn dread and awe alike. We propose a physically-based approach to describe the 3D development of cyclones in a visually convincing and physically plausible manner. Our approach allows us to capture large-scale heat and water continuity, turbulent microphysical dynamics of hydrometeors, and mesoscale cyclonic processes within the planetary boundary layer. Modeling these processes enables us to simulate multiple hurricane and tornado phenomena. We evaluate our simulations quantitatively by comparing to real data from storm soundings and observations of hurricane landfall from climatology research. Additionally, qualitative comparisons to previous methods are performed to validate the different parts of our scheme. In summary, our model simulates cyclogenesis in a comprehensive way that allows us to interactively render animations of some of the most complex weather events.

Wildfires are a complex physical phenomenon that involves the combustion of a variety of flammable materials ranging from fallen leaves and dried twigs to decomposing organic material and living flora. All these materials can potentially act as fuel with different properties that determine the progress and severity of a wildfire. In this paper, we propose a novel approach for simulating the dynamic interaction between the varying components of a wildfire, including processes of convection, combustion and heat transfer between vegetation, soil and atmosphere. We propose a novel representation of vegetation that includes detailed branch geometry, fuel moisture, and distribution of grass, fine fuel, and duff. Furthermore, we model the ignition, generation, and transport of fire by firebrands and embers. This allows simulating and rendering virtual 3D wildfires that realistically capture key aspects of the process, such as progressions from ground to crown fires, the impact of embers carried by wind, and the effects of fire barriers and other human intervention methods. We evaluate our approach through numerous experiments and based on comparisons to real-world wildfire data.

Architectural surface panelling often requires fabricating molds for panels, a process that can be cost-inefficient and material-wasteful when using traditional methods such as CNC milling. In this paper, we introduce a novel solution to generating molds for efficiently fabricating architectural panels. At the core of our method is a machine that utilizes a deflatable membrane as a flexible mold. By adjusting the deflation level and boundary element positions, the membrane can be reconfigured into various shapes, allowing for mass customization with significantly lower overhead costs. We devise an efficient algorithm that works in sync with our flexible mold machine that optimizes the placement of customizable boundary element positions, ensuring the fabricated panel matches the geometry of a given input shape: (1) Using a quadratic Weingarten surface arising from a natural assumption on the membrane's stress, we can approximate the initial placement of the boundary element from the input shape's geometry; (2) we solve the inverse problem with a simulator-in-the-loop optimizer by searching for the optimal placement of boundary curves with sensitivity analysis. We validate our approach by fabricating baseline panels and a facade with a wide range of curvature profiles, providing a detailed numerical analysis on simulation and fabrication, demonstrating significant advantages in cost and flexibility.

Plants are among the most complex objects to be modeled in computer graphics. While a large body of work is concerned with structural modeling and the dynamic reaction to external forces, our work focuses on the dynamic deformation caused by plant internal wilting processes. To this end, we motivate the simulation of water transport inside the plant which is a key driver of the wilting process. We then map the change of water content in individual plant parts to branch stiffness values and obtain the wilted plant shape through a position based dynamics simulation. We show, that our approach can recreate measured wilting processes and does so with a higher fidelity than approaches ignoring the internal water flow. Realistic plant wilting is not only important in a computer graphics context but can also aid the development of machine learning algorithms in agricultural applications through the generation of synthetic training data.

Computer graphics has dedicated a considerable amount of effort to generating realistic models of trees and plants. Many existing methods leverage procedural modeling algorithms - that often consider biological findings - to generate branching structures of individual trees. While the realism of tree models generated by these algorithms steadily increases, most approaches neglect to model the root system of trees. However, the root system not only adds to the visual realism of tree models but also plays an important role in the development of trees. In this paper, we advance tree modeling in the following ways: First, we define a physically-plausible soil model to simulate resource gradients, such as water and nutrients. Second, we propose a novel developmental procedural model for tree roots that enables us to emergently develop root systems that adapt to various soil types. Third, we define long-distance signaling to coordinate the development of shoots and roots. We show that our advanced procedural model of tree development enables - for the first time - the generation of trees with their root systems.

Ferrofluids are oil-based liquids containing magnetic particles that interact with magnetic fields without solidifying. Leveraging the exploration of new applications of these promising materials (such as in optics, medicine and engineering) requires high fidelity modeling and simulation capabilities in order to accurately explore ferrofluids in silico. While recent work addressed the macroscopic simulation of large-scale ferrofluids using smoothed-particle hydrodynamics (SPH), such simulations are computationally expensive. In their work, the Kelvin force model has been used to calculate interactions between different SPH particles. The application of this model results in a force pointing outwards with respect to the fluid surface causing significant levitation problems. This drawback limits the application of more advanced and efficient SPH frameworks such as divergence-free SPH (DFSPH) or implicit incompressible SPH (IISPH). In this contribution, we propose a current loop magnetic force model which enables the fast macroscopic simulation of ferrofluids. Our new force model results in a force term pointing inwards allowing for more stable and fast simulations of ferrofluids using DFSPH and IISPH.

We present RLSS: a reinforcement learning algorithm for sequential scene generation. This is based on employing the proximal policy optimization (PPO) algorithm for generative problems. In particular, we consider how to effectively reduce the action space by including a greedy search algorithm in the learning process. Our experiments demonstrate that our method converges for a relatively large number of actions and learns to generate scenes with predefined design objectives. This approach is placing objects iteratively in the virtual scene. In each step, the network chooses which objects to place and selects positions which result in maximal reward. A high reward is assigned if the last action resulted in desired properties whereas the violation of constraints is penalized. We demonstrate the capability of our method to generate plausible and diverse scenes efficiently by solving indoor planning problems and generating Angry Birds levels.

One of the greatest challenges to mankind is understanding the underlying principles of climate change. Over the last years, the role of forests in climate change has received increased attention. This is due to the observation that not only the atmosphere has a principal impact on vegetation growth but also that vegetation is contributing to local variations of weather resulting in diverse microclimates. The interconnection of plant ecosystems and weather is described and studied as ecoclimates. In this work we take steps towards simulating ecoclimates by modeling the feedback loops between vegetation, soil, and atmosphere. In contrast to existing methods that only describe the climate at a global scale, our model aims at simulating local variations of climate. Specifically, we model tree growth interactively in response to gradients of water, temperature and light. As a result, we are able to capture a range of ecoclimate phenomena that have not been modeled before, including geomorphic controls, forest edge effects, the Foehn effect and spatial vegetation patterning. To validate the plausibility of our method we conduct a comparative analysis to studies from ecology and climatology. Consequently, our method advances the state-of-the-art of generating highly realistic outdoor landscapes of vegetation.

Multigrid methods are quite efficient for solving the pressure Poisson equation in simulations of incompressible flow. However, for viscous liquids, geometric multigrid turned out to be less efficient for solving the variational viscosity equation. In this contribution, we present an Unsmoothed Aggregation Algebraic MultiGrid (UAAMG) method with a multi-color Gauss-Seidel smoother, which consistently solves the variational viscosity equation in a few iterations for various material parameters. Moreover, we augment the OpenVDB data structure with Intel SIMD intrinsic functions to perform sparse matrix-vector multiplications efficiently on all multigrid levels. Our framework is 2.0 to 14.6 times faster compared to the state-of-the-art adaptive octree solver in commercial software for the large-scale simulation of both non-viscous and viscous flow. The code is available at http://computationalsciences.org/publications/shao-2022-multigrid.html.

Iterative solvers are widely used to accurately simulate physical systems. These solvers require initial guesses to generate a sequence of improving approximate solutions. In this contribution, we introduce a novel method to accelerate iterative solvers for rod dynamics with graph networks (GNs) by predicting the initial guesses to reduce the number of iterations. Unlike existing methods that aim to learn physical systems in an end-to-end manner, our approach guarantees long-term stability and therefore leads to more accurate solutions. Furthermore, our method improves the run time performance of traditional iterative solvers for rod dynamics. To explore our method we make use of position-based dynamics (PBD) as a common solver for physical systems and evaluate it by simulating the dynamics of elastic rods. Our approach is able to generalize across different initial conditions, discretizations, and realistic material properties. We demonstrate that it also performs well when taking discontinuous effects into account such as collisions between individual rods. Finally, to illustrate the scalability of our approach, we simulate complex 3D tree models composed of over a thousand individual branch segments swaying in wind fields.

Resulting from changing climatic conditions, wildfires have become an existential threat across various countries around the world. The complex dynamics paired with their often rapid progression renders wildfires an often disastrous natural phenomenon that is difficult to predict and to counteract. In this paper we present a novel method for simulating wildfires with the goal to realistically capture the combustion process of individual trees and the resulting propagation of fires at the scale of forests. We rely on a state-of-the-art modeling approach for large-scale ecosystems that enables us to represent each plant as a detailed 3D geometric model. We introduce a novel mathematical formulation for the combustion process of plants - also considering effects such as heat transfer, char insulation, and mass loss - as well as for the propagation of fire through the entire ecosystem. Compared to other wildfire simulations which employ geometric representations of plants such as cones or cylinders, our detailed 3D tree models enable us to simulate the interplay of geometric variations of branching structures and the dynamics of fire and wood combustion. Our simulation runs at interactive rates and thereby provides a convenient way to explore different conditions that affect wildfires, ranging from terrain elevation profiles and ecosystem compositions to various measures against wildfires, such as cutting down trees as firebreaks, the application of fire retardant, or the simulation of rain.

Due to the complex interplay of various meteorological phenomena, simulating weather is a challenging and open research problem. In this contribution, we propose a novel physics-based model that enables simulating weather at interactive rates. By considering atmosphere and pedosphere we can define the hydrologic cycle - and consequently weather - in unprecedented detail. Specifically, our model captures different warm and cold clouds, such as mammatus, hole-punch, multi-layer, and cumulonimbus clouds as well as their dynamic transitions. We also model different precipitation types, such as rain, snow, and graupel by introducing a comprehensive microphysics scheme. The Wegener-Bergeron-Findeisen process is incorporated into our Kessler-type microphysics formulation covering ice crystal growth occurring in mixed-phase clouds. Moreover, we model the water run-off from the ground surface, the infiltration into the soil, and its subsequent evaporation back to the atmosphere. We account for daily temperature changes, as well as heat transfer between pedosphere and atmosphere leading to a complex feedback loop. Our framework enables us to interactively explore various complex weather phenomena. Our results are assessed visually and validated by simulating weatherscapes for various setups covering different precipitation events and environments, by showcasing the hydrologic cycle, and by reproducing common effects such as Foehn winds. We also provide quantitative evaluations creating high-precipitation cumulonimbus clouds by prescribing atmospheric conditions based on infrared satellite observations. With our model we can generate dynamic 3D scenes of weatherscapes with high visual fidelity and even nowcast real weather conditions as simulations by streaming weather data into our framework.

The simulation of large open water surface is challenging using a uniform volumetric discretization of the Navier-Stokes equations. Simulating water splashes near moving objects, which height field methods for water waves cannot capture, necessitates high resolutions. Such simulations can be carried out using the Fluid-Implicit-Particle (FLIP) method. However, the FLIP method is not efficient for the long-lasting water waves that propagate to long distances, which require sufficient depth for a correct dispersion relationship. This paper presents a new method to tackle this dilemma through an efficient hybridization of volumetric and surface-based advection-projection discretizations. We design a hybrid time-stepping algorithm that combines a FLIP domain and an adaptively remeshed Boundary Element Method (BEM) domain for the incompressible Euler equations. The resulting framework captures the detailed water splashes near moving objects with the FLIP method, and produces convincing water waves with correct dispersion relationships at modest additional costs.

We introduce a novel method for reconstructing the 3D geometry of botanical trees from single photographs. Faithfully reconstructing a tree from single-view sensor data is a challenging and open problem because many possible 3D trees exist that fit the tree's shape observed from a single view. We address this challenge by defining a reconstruction pipeline based on three neural networks. The networks simultaneously mask out trees in input photographs, identify a tree's species, and obtain its 3D radial bounding volume - our novel 3D representation for botanical trees. Radial bounding volumes (RBV) are used to orchestrate a procedural model primed on learned parameters to grow a tree that matches the main branching structure and the overall shape of the captured tree. While the RBV allows us to faithfully reconstruct the main branching structure, we use the procedural model's morphological constraints to generate realistic branching for the tree crown. This constraints the number of solutions of tree models for a given photograph of a tree. We show that our method reconstructs various tree species even when the trees are captured in front of complex backgrounds. Moreover, although our neural networks have been trained on synthetic data with data augmentation, we show that our pipeline performs well for real tree photographs. We evaluate the reconstructed geometries with several metrics, including leaf area index and maximum radial tree distances.

The complex interplay of a number of physical and meteorological phenomena makes simulating clouds a challenging and open research problem. We explore a physically accurate model for simulating clouds and the dynamics of their transitions. We propose first-principle formulations for computing buoyancy and air pressure that allow us to simulate the variations of atmospheric density and varying temperature gradients. Our simulation allows us to model various cloud types, such as cumulus, stratus, and stratoscumulus, and their realistic formations caused by changes in the atmosphere. Moreover, we are able to simulate large-scale cloud super cells - clusters of cumulonimbus formations - that are commonly present during thunderstorms. To enable the efficient exploration of these stormscapes, we propose a lightweight set of high-level parameters that allow us to intuitively explore cloud formations and dynamics. Our method allows us to simulate cloud formations of up to about 20 km × 20 km extents at interactive rates. We explore the capabilities of physically accurate and yet interactive cloud simulations by showing numerous examples and by coupling our model with atmosphere measurements of real-time weather services to simulate cloud formations in the now. Finally, we quantitatively assess our model with cloud fraction profiles, a common measure for comparing cloud types.

We devise a novel surface-only approach for simulating the three dimensional free-surface flow of incompressible, inviscid, and linearly magnetizable ferrofluids. A Lagrangian velocity field is stored on a triangle mesh capturing the fluid's surface. The two key problems associated with the dynamic simulation of the fluid's interesting geometry are the magnetization process transitioning the fluid from a non-magnetic into a magnetic material, and the evaluation of magnetic forces. In this regard, our key observation is that for linearly incompressible ferrofluids, their magnetization and application of magnetic forces only require knowledge about the position of the fluids' boundary. Consequently, our approach employs a boundary element method solving the magnetization problem and evaluating the so-called magnetic pressure required for the force evaluation. The magnetic pressure is added to the Dirichlet boundary condition of a surface-only liquids solver carrying out the dynamical simulation. By only considering the fluid's surface in contrast to its whole volume, we end up with an efficient approach enabling more complex and realistic ferrofluids to be explored in the digital domain without compromising efficiency. Our approach allows for the use of physical parameters leading to accurate simulations as demonstrated in qualitative and quantitative evaluations.

We present an approach to the accurate and efficient large-scale simulation of the complex dynamics of ferrofluids based on physical principles. Ferrofluids are liquids containing magnetic particles that react to an external magnetic field without solidifying. In this contribution, we employ smooth magnets to simulate ferrofluids in contrast to previous methods based on the finite element method or point magnets. We solve the magnetization using the analytical solution of the smooth magnets' field, and derive the bounded magnetic force formulas addressing particle penetration. We integrate the magnetic field and force evaluations into the fast multipole method allowing for efficient large-scale simulations of ferrofluids. The presented simulations are well reproducible since our approach can be easily incorporated into a framework implementing a Fast Multipole Method and a Smoothed Particle Hydrodynamics fluid solver with surface tension. We provide a detailed analysis of our approach and validate our results against real wet lab experiments. This work can potentially open the door for a deeper understanding of ferrofluids and for the identification of new areas of applications of these materials.

Due to the enormous amount of detail and the interplay of various biological phenomena, modeling realistic ecosystems of trees and other plants is a challenging and open problem. Previous research on modeling plant ecologies has focused on representations to handle this complexity, mostly through geometric simplifications, such as points or billboards. In this paper we describe a multi-scale method to design large-scale ecosystems with individual plants that are realistically modeled and faithfully capture biological features, such as growth, plant interactions, different types of tropism, and the competition for resources. Our approach is based on leveraging inter- and intra-plant self-similarities for efficiently modeling plant geometry. We focus on the interactive design of plant ecosystems of up to 500K plants, while adhering to biological priors known in forestry and botany research. The introduced parameter space supports modeling properties of nine distinct plant ecologies while each plant is represented as a 3D surface mesh. The capabilities of our framework are illustrated through numerous models of forests, individual plants, and validations.

For a nonlinear ordinary differential equation solved with respect to the highest order derivative and rational in the other derivatives and in the independent variable, we devise two algorithms to check if the equation can be reduced to a linear one by a point transformation of the dependent and independent variables. The first algorithm is based on a construction of the Lie point symmetry algebra and on the computation of its derived algebra. The second algorithm exploits the differential Thomas decomposition and allows not only to test the linearizability, but also to generate a system of nonlinear partial differential equations that determines the point transformation and the coefficients of the linearized equation. The implementation of both algorithms is discussed and their application is illustrated using several examples.

We present a new integration algorithm for the accurate and efficient solution of stiff elastodynamic problems governed by the second-order ordinary differential equations of structural mechanics. Current methods have the shortcoming that their performance is highly dependent on the numerical stiffness of the underlying system that often leads to unrealistic behavior or a significant loss of efficiency. To overcome these limitations, we present a new integration method which is based on a mathematical reformulation of the underlying differential equations, an exponential treatment of the full nonlinear forcing operator as opposed to more standard partially implicit or exponential approaches, and the utilization of the concept of stiff accuracy which ensures that the efficiency of the simulations is significantly less sensitive to increased stiffness. As a consequence, we are able to tremendously accelerate the simulation of stiff systems compared to established integrators and significantly increase the overall accuracy. The advantageous behavior of this approach is demonstrated on a broad spectrum of complex examples like deformable bodies, textiles, bristles, and human hair. Our easily parallelizable integrator enables more complex and realistic models to be explored in visual computing without compromising efficiency.

We present a novel method for the combustion of botanical tree models. Tree models are represented as connected particles for the branching structure and a polygonal surface mesh for the combustion. Each particle stores biological and physical attributes that drive the kinetic behavior of a plant and the exothermic reaction of the combustion. Coupled with realistic physics for rods, the particles enable dynamic branch motions. We model material properties, such as moisture and charring behavior, and associate them with individual particles. The combustion is efficiently processed in the surface domain of the tree model on a polygonal mesh. A user can dynamically interact with the model by initiating fires and by inducing stress on branches. The flames realistically propagate through the tree model by consuming the available resources. Our method runs at interactive rates and supports multiple tree instances in parallel. We demonstrate the effectiveness of our approach through numerous examples and evaluate its plausibility against the combustion of real wood samples.

We investigate numerical integration of ordinary differential equations (ODEs) for Hamiltonian Monte Carlo (HMC). High-quality integration is crucial for designing efficient and effective proposals for HMC. While the standard method is leapfrog (Stormer-Verlet) integration, we propose the use of an exponential integrator, which is robust to stiff ODEs with highly-oscillatory components. This oscillation is difficult to reproduce using leapfrog integration, even with carefully selected integration parameters and preconditioning. Concretely, we use a Gaussian distribution approximation to segregate stiff components of the ODE. We integrate this term analytically for stability and account for deviation from the approximation using variation of constants. We consider various ways to derive Gaussian approximations and conduct extensive empirical studies applying the proposed “exponential HMC” to several benchmarked learning problems. We compare to state-of-the-art methods for improving leapfrog HMC and demonstrate the advantages of our method in generating many effective samples with high acceptance rates in short running times.

We investigate the application of exponential integrators to stiff elastodynamic problems governed by second-order differential equations. Classical explicit numerical integration schemes have the shortcoming that the stepsizes are limited by the highest frequency that occurs within the solution spectrum of the governing equations, while implicit methods suffer from an inevitable and mostly uncontrollable artificial viscosity that often leads to a nonphysical behavior. In order to overcome these specific detriments, we devise an appropriate class of exponential integrators that solve the stiff part of the governing equations of motion by employing a closed-form solution. As a consequence, we are able to handle up to three orders of magnitude larger time-steps as with conventional implicit integrators and at the same time achieve a tremendous increase in the overall long-term stability due to a strict energy conservation. The advantageous behavior of our approach is demonstrated on a broad spectrum of complex deformable models like fibers, textiles, and solids, including collision response, friction, and damping.