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Systems consisting of interacting agents are prevalent in the world, ranging from dynamical systems in physics to complex biological networks. To build systems which can interact robustly in the real world, it is thus important to be able to infer the precise interactions governing such systems. Existing approaches typically dis- cover such interactions by explicitly modeling the feed-forward dynamics of the trajectories. In this work, we propose Neural Interaction Inference with Potentials (NIIP) as an alternative approach to discover such interactions that enables greater flexibility in trajectory modeling: it discovers a set of relational potentials, represented as energy functions, which when minimized reconstruct the original trajectory. NIIP assigns low energy to the subset of trajectories which respect the relational constraints observed. We illustrate that with these representations NIIP displays unique capabilities in test-time. First, it allows trajectory manipulation, such as interchanging interaction types across separately trained models, as well as trajectory forecasting. Additionally, it allows adding external hand-crafted potentials at test-time. Finally, NIIP enables the detection of out-of-distribution samples and anomalies without explicit training. 

One of the long-term objectives of Machine Learning is to endow machines with the capacity of structuring and interpreting the world as we do. This is particularly challenging in scenes involving time series, such as video sequences, since seemingly different data can correspond to the same underlying dynamics. Recent approaches seek to decompose video sequences into their composing objects, attributes and dynamics in a self-supervised fashion, thus simplifying the task of learning suitable features that can be used to analyze each component. While existing methods can successfully disentangle dynamics from other components, there have been relatively few efforts in learning parsimonious representations of these underlying dynamics. In this paper, motivated by recent advances in non-linear identification, we propose a method to decompose a video into moving objects, their attributes and the dynamic modes of their trajectories. We model video dynamics as the output of a Koopman operator to be learned from the available data. In this context, the dynamic information contained in the scene is encapsulated in the eigenvalues and eigenvectors of the Koopman operator, providing an interpretable and parsimonious representation. We show that such decomposition can be used for instance to perform video analytics, predict future frames or generate synthetic video. We test our framework in a variety of datasets that encompass different dynamic scenarios, while illustrating the novel features that emerge from our dynamic modes decomposition: Video dynamics interpretation and user manipulation at test-time. We successfully forecast challenging object trajectories from pixels, achieving competitive performance while drawing useful insights. 

Systems consisting of interacting agents are prevalent in the world, ranging from dynamical systems in physics to complex biological networks. To build systems which can interact robustly in the real world, it is thus important to be able to infer the precise interactions governing such systems. Existing approaches typically discover such interactions by explicitly modeling the feed-forward dynamics of the trajectories. In this work, we propose Neural Interaction Inference with Potentials (NIIP) as an alternative approach to discover such interactions that enables greater flexibility in trajectory modeling: it discovers a set of relational potentials, represented as energy functions, which when minimized reconstruct the original trajectory. NIIP assigns low energy to the subset of trajectories which respect the relational constraints observed. We illustrate that with these representations NIIP displays unique capabilities in test-time. First, it allows trajectory manipulation, such as interchanging interaction types across separately trained models, as well as trajectory forecasting. Additionally, it allows adding external hand-crafted potentials at test-time. Finally, NIIP enables the detection of out-of-distribution samples and anomalies without explicit training. 

Water contamination by nitrogen and phosphorus ions has a direct consequence of eutrophication to the ecosystem. The objective of this study is to investigate the production of hydrochars by acetic acid or sodium hydroxide assisted hydrothermal carbonization (HTC), various activation methods, and the potential of hydrochar as an adsorbent to remove NH4+-N and PO43--P from wastewater. The results showed that acetic acid or sodium hydroxide assisted HTC and activation with magnesium chloride or air could improve the surface properties of hydrochar. Acetic acid modification generated extensive oxygenated functional groups, while sodium hydroxide modification produced hydrochar with a high N/C ratio and surface aromaticity. Treating hydrochar with magnesium chloride could impregnate nano-magnesium particles on the hydrochar, thereby improving the ability to remove N and P. Air activation of hydrochar resulted in more oxygen containing functional groups. The NH4+-N and PO43--P adsorption capacities of these hydrochars ranged from 92.6 to 122.4mg/g and 1.6 to 15.8mg/g, respectively. The adsorption capacity of hydrochars in swine wastewater is similar to the results of artificial wastewater. The results suggested that Mg-nanoparticle dispersion and oxygen-containing functional groups played a major role in adsorption than ion exchange and physisorption. 

Water contamination by nitrogen and phosphorus ions has a direct consequence of eutrophication to the ecosystem. The objective of this study is to investigate the production of hydrochars by acetic acid or sodium hydroxide assisted hydrothermal carbonization (HTC), various activation methods, and the potential of hydrochar as an adsorbent to remove NH4+-N and PO43−-P from wastewater. The results showed that acetic acid or sodium hydroxide assisted HTC and activation with magnesium chloride or air could improve the surface properties of hydrochar. Acetic acid modification generated extensive oxygenated functional groups, while sodium hydroxide modification produced hydrochar with a high N/C ratio and surface aromaticity. Treating hydrochar with magnesium chloride could impregnate nano-magnesium particles on the hydrochar, thereby improving the ability to remove N and P. Air activation of hydrochar resulted in more oxygen containing functional groups. The NH4+-N and PO43−-P adsorption capacities of these hydrochars ranged from 92.6 to 122.4mg/g and 1.6 to 15.8mg/g, respectively. The adsorption capacity of hydrochars in swine wastewater is similar to the results of artificial wastewater. The results suggested that Mg-nanoparticle dispersion and oxygen-containing functional groups played a major role in adsorption than ion exchange and physisorption.